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Delay-Dependent Switched Filtering

  • Magdi S. Mahmoud
Chapter

Abstract

In this chapter, the filtering problem for a class of discrete-time switched systems with state delays is thoroughly investigated. We will focus on discrete-time systems. Attention will be equally focused on the design of stable filters guaranteeing different prescribed performance criteria including the \({\cal L}_{2}\) sense and in the \({\cal L}_{2}-{\cal L}_{\infty}\) sense. In all cases, switched Lyapunov functionals are employed to derive sufficient conditions for the solvability of the filtering problem and expressed in terms of linear matrix inequalities (LMIs).

Keywords

Linear Matrix Inequality Filter System State Delay Filter Design Gain Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 72.
    Fu, M., C. E. de Souza and L. Xie, \(\mathcal{H}_{\infty}\)-Estimation for Uncertain Systems, Int. J. Robust Nonlinear Contr., vol. 2, 1992, pp. 87–105.MATHCrossRefGoogle Scholar
  2. 179.
    Lee, C. S. and G. Leitmann, Continuous Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Linear Delay Systems: An Application to River Pollution Control, Comput. Math. Model., vol. 16, 1988, pp. 929–938.MathSciNetMATHGoogle Scholar
  3. 218.
    Mahmoud, M. S., Resilient Linear Filtering of Uncertain Systems, Automatica, vol. 40, no. 10, 2004, pp. 1797–1802.MathSciNetMATHCrossRefGoogle Scholar
  4. 237.
    Mahmoud, M. S. and Abdulla Ismail, New Results on Delay-Dependent Control of Time-Delay Systems, IEEE Trans. Automat. Contr., vol. 50, 2005, pp. 95–100.CrossRefGoogle Scholar
  5. 2.
    Alessandri, A., M. Baglietto and G. Battistelli, Leunberger Observers for Switching Discrete-Time Linear Systems, Proceedings of the 44th IEEE CDC, Seville, Spain, 2005, pp. 7014–7019.Google Scholar
  6. 222.
    Mahmoud, M. S., New Results on Robust Control Design of Discrete-Time Uncertain Systems, IEE Proc. Contr. Theory Appl., vol. 152, 2005, pp. 453–459.CrossRefGoogle Scholar
  7. 162.
    Kharitonov, V. L. and D. Melchor-Aguilar, Delay-Dependent Stability Conditions, Syst. Contr. Lett., vol. 40, 2000, pp. 71–76.MathSciNetMATHCrossRefGoogle Scholar
  8. 128.
    He, Y., M. Wu, J. H. She and Y. C. Wang, Parameter-Dependent Lyapunov Functional for Stability of Time-Delay Systems with Polytopic Uncertainties, IEEE Trans. Automat. Contr., vol. 49, no. 5, 2004, pp. 828–832.CrossRefGoogle Scholar
  9. 431.
    Zhang, H., C. Li and X. Liao, Stability Analysis and \(\mathcal{H}_{\infty}\) Controller Design of Fuzzy Large-Scale Systems based on Piecewise Lyapunov Functions, IEEE Trans. Syst. Man Cybern.-Part B, vol. 36, 2006, pp. 685–698.CrossRefGoogle Scholar
  10. 151.
    Jiang, B. and F. N. Chowdhury, Fault Estimation and Accommodation for Linear MIMO Discrete-Time Systems, IEEE Trans. Contr. Syst. Technol., vol. 13, no. 3, 2005, pp. 493–499.CrossRefGoogle Scholar
  11. 313.
    Ohtake, H., K. Tanaka and H. O. Wang, Switching Fuzzy Controller Design Based on Switching Lyapunov Function for a Class of Nonlinear Systems, IEEE Trans. Syst. Man Cybern.-Part B, vol. 36, 2006, pp. 13–23.CrossRefGoogle Scholar
  12. 253.
    Mahmoud, M. S. and M. F. Hassan, A Decentralized Water Quality Control Scheme, IEEE Trans. Syst. Man Cybern., vol. SMC-16, 1986, pp. 694–702.CrossRefGoogle Scholar
  13. 80.
    Gao, H. and C. Wang, Comments and Further Results on ’A Descriptor System Approach to \(\mathcal{H}_{\infty}\) Control of Linear Time-Delay Systems, IEEE Trans. Automat. Contr., vol. 48, no. 3, 2003, pp. 520–525.CrossRefGoogle Scholar
  14. 88.
    Geromel, J. C. and P. Colaneri, Stability and Stabilization of Continuous-Time Switched Linear Systems, SIAM J. Contr. Optim., vol. 45, no. 5, 2006, pp. 1915–1930.MathSciNetMATHCrossRefGoogle Scholar
  15. 62.
    Feng, G., Robust Filtering Design of Piecewise Discrete-Time Linear Systems, IEEE Trans. Signal Process., vol. 53, 2005, pp. 599–605.MathSciNetCrossRefGoogle Scholar
  16. 161.
    Khargonekar P. P. and M. A. Rotea, Mixed \(\mathcal{H}_{2}/\mathcal{H}_{\infty}\) Control: A Convex Optimization Approach, IEEE Trans. Automat. Contr., vol. 36, 1991, pp. 824–837.MathSciNetMATHCrossRefGoogle Scholar
  17. 385.
    Wang, M., B. Chen and P. Shi, Adaptive Neural Control for a Class of Perturbed Strict-Feedback Nonlinear Time-Delay Systems, IEEE Trans. Syst. Man Cybern.-Part B, vol. 38, 2008, pp. 721–726.CrossRefGoogle Scholar
  18. 200.
    Liu, P.-L. and T.-J. Su, Robust Stability of Interval Time-delay Systems with Delay-Dependence, Syst. Contr. Lett., vol. 33, 1998, pp. 231–239.MathSciNetMATHCrossRefGoogle Scholar
  19. 101.
    Gu, K., An Integral Inequality in the Stability Problem of Time-Delay Systems, Proceedings of 39th IEEE Conference on Decision and Control, Sydney, 2000, pp. 2805–2810.Google Scholar
  20. 98.
    . Gouaisbaut, F. and D. Peaucelle, Delay-Dependent Robust Stability of Time Delay Systems, Proceedings of the 5th IFAC Symposium on Robust Control Design, Toulouse, France, vol. 2, July 57, 2006.Google Scholar
  21. 193.
    Liberzon, D. and A. Morse, Basic Problems in Stability and Design of Switched Systems, IEEE Contr. Syst. Mag., vol. 19, no. 5, 1999, pp. 59–70.CrossRefGoogle Scholar
  22. 97.
    Gouaisbaut, F. and D. Peaucelle, A Note on Stability of Time Delay Systems, Proceedings of the 5th IFAC Symposium on Robust Control Design, Toulouse, France, vol. 2, July 57, 2006.Google Scholar
  23. 201.
    Liu, F. and S. Y. Zhang, Robust Decentralized Output Feedback Control of Similar Composite System with Uncertainties Unknown, Proceedings of the American Control Conference, vol. 6, Boston, MA, 1999, pp. 3838–3842.Google Scholar
  24. 441.
    Zhao, J. and G. M. Dimirovski, Quadratic Stability of a Class of Switched Nonlinear Systems, IEEE Trans. on Automat. Contr., vol. 49, 2004, pp. 574–578.MathSciNetCrossRefGoogle Scholar
  25. 235.
    Mahmoud, M. S. and Abdulla Ismail, Role of Delay in Networked Control Systems, Proceedings of the 10th IEEE International Conference on Electronics, Circuits and Systems, University of Sharaja, UAE, December 15–17, 2003, pp. 40–43.Google Scholar
  26. 176.
    Kulkarni, V., M. Jun and J. Hespanha, Piecewise Quadratic Lyapunov Functions for Piecewise Affine Time-Delay Systems, Proceedings of the ACCC, Boston, MA, 2004, pp. 2975–2984.Google Scholar
  27. 207.
    Mahmoud, M. S., Guaranteed Stabilization of Interconnected Discrete-Time Systems, Int. J. Syst. Sci., vol. 26, no. 1, 1995, pp. 337–358.MATHCrossRefGoogle Scholar
  28. 122.
    He, Y., G. P. Liu, D. Rees and M. Wu, \(\mathcal{H}_{\infty}\) Filtering for Discrete-Time Systems with Time-Varying Delay, Signal Process., vol. 89, no. 3, 2009, pp. 275–282.MATHCrossRefGoogle Scholar
  29. 87.
    Geromel, J. C., Optimal Linear Filtering with Parameter Uncertainty, IEEE Trans. Signal Process., vol. 47, 1999, pp. 168–175.MATHCrossRefGoogle Scholar
  30. 197.
    Lin, D., X. Liu and S. Zhong, Delay-Dependent Robust Stability and Control Synthesis for Uncertain Switched Neutral Systems with Mixed Delays, Appl. Math. Comput., vol. 202, 2008, pp. 828–839.MathSciNetCrossRefGoogle Scholar
  31. 71.
    Fridman, E. and U. Shaked, Delay-Dependent \(\mathcal{H}_{\infty}\) Control of Uncertain Discrete Delay Systems, Eur. J. Contr., vol. 11, 2005, pp. 29–37.MathSciNetCrossRefGoogle Scholar
  32. 108.
    Hale, J. K. and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, Berlin, 1993.MATHGoogle Scholar
  33. 425.
    Zhai, G. S., Y. Sun, X. K. Chen and N. M. Anthony, Stability and \(\mathcal{L}_{2}\) Gain Analysis for Switched Symmetric Systems with Time Delay, Proceedings of the American Control Conference, Portland, OR, 2003, pp. 2682–2687.Google Scholar
  34. 185.
    Leite, V. J., S. Tarbouriech and P. L. D. Peres, A Convex Approach for Robust State\(=\)Feedback Control of Discrete-Time Systems with State Delay, Proceedings of the American Control Conference, Boston, MA, June 30 – July 2, 2004, pp. 2870–2875.Google Scholar
  35. 110.
    Han, Q.-L., A Descriptor System Approach to Robust Stability of Uncertain Neutral Systems with Discrete and Distributed Delays, Proceedings of the American Control Conference, Denver, vol. 2, June 2003, pp. 5098–5103.Google Scholar
  36. 214.
    Mahmoud, M. S., Delay-Dependent Robust Stability and Stabilization for Systems with Mismatched Uncertainties, IMA J. Math Contr. Inf., vol. 17, 2000, pp. 309–323.MATHCrossRefGoogle Scholar
  37. 219.
    Mahmoud, M. S., Robust Linear Filtering of Uncertain Systems, Automatica, vol. 40, 2004, pp. 1797–1802.MATHCrossRefGoogle Scholar
  38. 282.
    Mahmoud, M. S., P. Shi and A. Ismail, Robust Kalman Filtering for Discrete-Time Markovian Jump systems with Parameter Uncertainty, J. Comput. Appl. Math., vol. 169, no. 1, 2004, pp. 53–69.MathSciNetMATHCrossRefGoogle Scholar
  39. 346.
    Shi, P., M. Karan and Y. Kaya, Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities, Circuits Syst. Signal Process., vol. 24, no. 2, 2005, pp. 135–150.MathSciNetMATHCrossRefGoogle Scholar
  40. 63.
    Feng, G., Stability Analysis of Piecewise Discrete-Time Linear Systems, IEEE Trans. Automat. Contr., vol. 47, 2002, pp. 1108–1112.CrossRefGoogle Scholar
  41. 123.
    He, Y., Q. G. Wang, C. Lin and M. Wu, Augmented Lyapunov Functional and Delay-Dependent Stability Criteria for Neutral Systems, Int. J. Robust Nonlinear Contr., vol. 15, no. 8, 2005, pp. 923–933.MathSciNetMATHCrossRefGoogle Scholar
  42. 124.
    He, Y., Q. G. Wang, L. H. Xie and C. Lin, Further Improvement of Free-Weighting Matrices Technique for Systems with Time-Varying Delay, IEEE Trans. Automat. Contr., vol. 52, no. 2, 2007, pp. 293–299.MathSciNetCrossRefGoogle Scholar
  43. 206.
    Mahmoud, M. S., Output Feedback Stabilization of Uncertain Systems with State Delay. in Control and Dynamic Systems Series, vol. 63, Leondes, C. T. (Editor), Academic, New York, NY, 1994, pp. 197–257.Google Scholar
  44. 426.
    Zhai, G., B. Shu, K. Yasuda and A. N. Michel, Disturbance Attenuation Properties of Time-Controlled Switched Systems, J. Franklin Inst., vol. 338, 2001, pp. 765–779.MathSciNetMATHCrossRefGoogle Scholar
  45. 192.
    Liberzon, D., Switching in Systems and Control, Birkhauser, Boston, MA, 2003.MATHCrossRefGoogle Scholar
  46. 223.
    Mahmoud, M. S., Resilient \(\mathcal{L}_{2}/\mathcal{L}_{\infty}\) Filtering of Polytopic Systems with State-Delays, Proc. IET Contr. Theory Appl., vol. 1, 2007, pp. 141–154.CrossRefGoogle Scholar
  47. 107.
    Haimes, Y. Y., Hierarchical Analyses of Water Resources Systems, McGraw-Hill, New York, NY, 1977.Google Scholar
  48. 390.
    Wu, H. N., Delay-Dependent Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems with State-Delay: A Fuzzy Lyapunov-Krasovskii Functional Approach, IEEE Trans. Syst. Man Cybern.-Part B, vol. 36, 2006, pp. 954–962.CrossRefGoogle Scholar
  49. 173.
    Kolmanovskii, V. B., S.-I. Niculescu and J. P. Richard, On the Lyapunov-Krasovskii Functionals for Stability Analysis of Linear Delay Systems, Int. J. Contr., vol. 72, 1999, pp. 374–384.MathSciNetMATHCrossRefGoogle Scholar
  50. 85.
    Gao, H., J. Lam, C. Wang and L. Wang, Delay-Dependent Output-Feedback Stabilization of Discrete-Time Systems with Time-varying State Delay, IEE Proc. Contr. Theory Appl., vol. 151, 2004, pp. 691–698.CrossRefGoogle Scholar
  51. 89.
    Geromel, J. C. and G. S. Deaecto, Switched State Feedback Control for Continuous-Time Uncertain Systems, Automatica, vol. 45, 2009, pp. 593–597.MathSciNetMATHCrossRefGoogle Scholar
  52. 160.
    Khalil, H. K., Nonlinear Systems, 3rd edn., Prentice Hall, Upper Saddle River, NJ, 2002.MATHGoogle Scholar
  53. 131.
    Henzinger, T. and S. Sastry, (Editors), Hybrid Systems: Computation and Control, Springer, New York, NY, 1990.Google Scholar
  54. 376.
    Trecate, G. F., F. A. Cuzzola, D. Mignone and M. Morari, Analysis of Discrete-Time Piecewise Affine and Hybrid Systems, Automatica, vol. 38, 2002, pp. 2139–2146.MATHCrossRefGoogle Scholar
  55. 438.
    Zhang, L., P. Shi, E.-K. Boukas and C. Wang, Robust \(\ell_{2}-\ell_{\infty}\) Filtering for Switched Linear Discrete Time-Delay Systems with Polytopic Uncertainties, IET Contr. Theory Appl., vol. 1, no. 3, 2007, pp. 722–730.MathSciNetCrossRefGoogle Scholar
  56. 81.
    Gao, H., Robust Filtering for Bilinear Uncertain Stochastic Discrete-Time Systems, IEEE Trans. Signal Process., vol. 50, no. 3, 2002, pp. 560–567.MathSciNetCrossRefGoogle Scholar
  57. 99.
    Grossman, R. L., A. P. Ravn and H. Rischel, (Editors), Hybrid Systems, Springer, New York, NY, 1993.Google Scholar
  58. 83.
    Gao, H., T. Chen and J. Lam, A New Delay System Approach to Network-based Control, Automatica, vol. 44, 2008, pp. 39–52.MathSciNetMATHCrossRefGoogle Scholar
  59. 428.
    Zhang, B. and S. Xu, Robust \(\mathcal{H}_{\infty}\) Filtering for Uncertain Discrete Piecewise Time-Delay Systems, Int. J. Contr., vol. 80, no. 4, 2007, pp. 636–645.MATHCrossRefGoogle Scholar
  60. 276.
    Mahmoud, M. S., M. F. Hassan and M. G. Darwish, Large Scale Control Systems: Theories and Techniques, Marcel Dekker, New York, NY, 1985.MATHGoogle Scholar
  61. 104.
    Gu, K. Q. and S. I. Niculescu, Further Remarks on Additional Dynamics in Various Model Transformations of Linear Delay Systems, IEEE Trans. Automat. Contr., vol. 46, 2001, pp. 497–500.MathSciNetMATHCrossRefGoogle Scholar
  62. 356.
    Sorenson, H., (Editor), Kalman Filtering: Theory and Applications, IEEE Press, New York, NY, 1985.Google Scholar
  63. 159.
    Kapila, V. and W. M. Haddad, Memoryless \(\mathcal{H}_{\infty}\) Controllers for Discrete-Time Systems with Time-Delay, Automatica, vol. 34, no. 5, 1998, pp. 1141–1144.MATHCrossRefGoogle Scholar
  64. 287.
    Mahmoud, M. S., L. Xie and Y. C. Soh, Robust Kalman Filtering for Discrete State-Delay Systems, IEE Proc. – Contr. Theory Appl., vol. 147, 2000, pp. 613–618.CrossRefGoogle Scholar
  65. 100.
    Gu, K. Q., Discretized Lyapunov Functional for Uncertain Systems with Multiple Time-Delay, Int. J. Contr., vol. 72, no. 16, 1999, pp. 1436–1445.MATHCrossRefGoogle Scholar
  66. 165.
    Kharitonov, V. L. and D. Melchor-Aguilar, Lyapunov-Krasovskii Functionals for Additional Dynamics, Int. J. Robust Nonlinear Contr., vol. 13, 2003, pp. 793–804.MathSciNetMATHCrossRefGoogle Scholar
  67. 157.
    Kailath T., Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.MATHGoogle Scholar
  68. 278.
    Mahmoud, M. S., M. N. Nounou and H. N. Nounou, Analysis and Synthesis of Uncertain Switching Discrete-Time Systems, IMA J. Math. Contr. Inf., vol. 23, no. 6, 2006, pp. 245–257.CrossRefGoogle Scholar
  69. 318.
    Palhares, R. M. and P. L. D. Peres, Robust Filtering with Guaranteed Energy-to-Peak Performance- An LMI Approach, Automatica, vol. 36, 2000, pp. 851–855.MathSciNetMATHCrossRefGoogle Scholar
  70. 291.
    Meyer, C., S. Schroder and R. W. De Doncker, Solid-State Circuits Breakers and Current Limiters for Medium-Voltage Systems having Distributed Power Systems, IEEE Trans. Power Electron., vol. 19, 2004, pp. 1333–1340.CrossRefGoogle Scholar
  71. 75.
    Gao, H., Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks with Mixed Mode-Dependent Time-Delays, IEEE Trans. Neural Netw., vol. 20, no. 7, 2009, pp. 1102–1116.CrossRefGoogle Scholar
  72. 175.
    Krogh, B. and N. Lynch, (Editors), Hybrid Systems: Computation and Control, Springer, New York, NY, 2000.MATHGoogle Scholar
  73. 169.
    Kim, S., S. A. Campbell and X. Z. Liu, Stability of a Class of Linear Switching Systems with Time-Delay, IEEE Trans. Circuits Syst., vol. 53, no. 2, 2006, pp. 384–393.MathSciNetCrossRefGoogle Scholar
  74. 77.
    Gao, H. and C. Wang, A Delay-Dependent Approach to Robust \(\mathcal{H}_{\infty}\) Filtering for Uncertain Discrete-Time State-Delayed Systems, IEEE Trans. Signal Process., vol. 52, no. 6, 2004, pp. 1631–1640.MathSciNetCrossRefGoogle Scholar
  75. 265.
    Mahmoud, M. S. and M. Zribi, \(\mathcal{H}_{\infty}\) Controllers for Time-Delay Systems using Linear Matrix Inequalities, J. Optim. Theory Appl., vol. 100, 1999, pp. 89–123.MathSciNetMATHCrossRefGoogle Scholar
  76. 3.
    Anderson, B. D. O. and J. B. Moore, Optimal Filtering, Prentice Hall, New York, NY, 1979.MATHGoogle Scholar
  77. 255.
    Mahmoud, M. S. and S. J. Saleh, Regulation of Water Quality Standards in Streams by Decentralized Control, Int. J. Contr., vol. 41, 1985, pp. 525–540.MathSciNetMATHCrossRefGoogle Scholar
  78. 194.
    Lien, C. H., K. W. Yu, Y. F. Lin, Y. J. Chung and L. Y. Chung, Global Exponential Stability for Uncertain Delayed Neural Networks of Neural Type with Mixed Time Delays, IEEE Trans. Syst. Man Cybern.-Part B, vol. 38, 2008, pp. 709–720.CrossRefGoogle Scholar
  79. 155.
    Jing, X. J., D. L. Tan and Y. C. Wang, An LMI Approach to Stability of Systems with Severe Time-Delay, IEEE Trans. Automat. Contr., vol. 49, no. 7, 2004, pp. 1192–1195.MathSciNetCrossRefGoogle Scholar
  80. 84.
    Gao, H., X. Meng and T. Chen, Stabilization of Networked Control Systems with New Delay Characterization, IEEE Trans. Automat. Contr., vol. 53, no. 9, 2008, pp. 2142–2148.MathSciNetCrossRefGoogle Scholar
  81. 147.
    Ji, Z. and L. Wang, Disturbance Attenuation of Uncertain Switched Linear Systems, Proceedings of the Conference on Decision and Control, Sydney, Australia, 2004, pp. 3708–3713.Google Scholar
  82. 263.
    Mahmoud, M. S. and L. H. Xie, Guaranteed Cost Control of Uncertain Discrete Systems with Delays, Int. J. Contr., vol. 73, 2000, pp. 105–114.MathSciNetMATHCrossRefGoogle Scholar
  83. 139.
    Hill, D. J. and P. J. Moylan, Dissipative Dynamical Systems: Basic Input-Output and State Properties, J. Franklin Inst., vol. 309, 1980, pp. 327–357.MathSciNetMATHCrossRefGoogle Scholar
  84. 78.
    Gao, H. and C. Wang, New Approaches to Robust \(\ell_{1}-\ell_{2}\) and \(\mathcal{H}_{\infty}\) Filtering for Uncertain Discrete Time Systems, Sci. China (Series E), vol. 33, 2003, pp. 695–706.Google Scholar
  85. 370.
    Sun, X., J. Zhao and D. J. Hill, Stability and \(\mathcal{L}_{2}\) Gain Analysis for Switched Delay Systems: A Delay-Dependent Method, Automatica, vol. 42, 2006, pp. 1769–1774.MathSciNetMATHCrossRefGoogle Scholar
  86. 152.
    Jiang, X. and Q. L. Han, \(\mathcal{H}_{\infty}\) Control for Linear Systems with Interval Time-Varying Delay, Automatica, vol. 41, no. 12, 2005, pp. 2099–2106.MathSciNetMATHCrossRefGoogle Scholar
  87. 305.
    Nagpal, K. M. and P. P. Khargonekar, Filtering and Smoothing in \(\mathcal{H}_{\infty}\) Setting, IEEE Trans. Automat. Contr., vol. 36, 1991, pp. 152–166.MathSciNetMATHCrossRefGoogle Scholar
  88. 250.
    Mahmoud, M. S. and A. A. Boujarwah, Robust \(\mathcal{H}_{\infty}\) Filtering for a Class of Linear Parameter-Varying Systems, IEEE Trans. Circuits Syst.-I, vol. 48, no. 9, 2001, pp. 1131–1138.MathSciNetMATHCrossRefGoogle Scholar
  89. 117.
    Hassan, M. F., M. S. Mahmoud and M. I. Younis, A Dynamic Leontief Modeling Approach to Management for Optimal Utilization in Water Resources Systems, IEEE Trans. Syst. Man Cybern., vol. SMC-11, 1981, pp. 552–558.CrossRefGoogle Scholar
  90. 73.
    Gahinet, P. and P. Apkarian, A Linear Matrix Inequality Approach to \(\mathcal{H}_{\infty}\) Control, Int. J. Robust Nonlinear Contr., vol. 4, 1994, pp. 421–448.MathSciNetMATHCrossRefGoogle Scholar
  91. 67.
    Fridman E. and U. Shaked, Stability and Guaranteed-Cost Control of Uncertain Discrete-Delay Systems, Int. J. Contr., vol. 78, 2005, pp. 235–246.MathSciNetMATHCrossRefGoogle Scholar
  92. 171.
    Kolomanovskii, V. and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer, New York, NY, 1992.CrossRefGoogle Scholar
  93. 42.
    Daafouz, J., P. Riedinger and C. Lung, Stability Analysis and Control Synthesis for Switched Systems: A Hybrid Lyapunov Function Approach, IEEE Trans. Automat. Contr., vol. 47, 2002, pp. 1883–1887.CrossRefGoogle Scholar
  94. 388.
    Wicks, M. A., P. Peleties and R. A. De Carlo, Construction of Piecewise Lyapunov Functions for Stabilizing Switched Systems, Proceedings of the 33rd Conference on Decision and Control, December 1994, pp. 3492–3497.Google Scholar
  95. 205.
    Mahmoud, M. S., Stabilizing Control for a Class of Uncertain Interconnected Systems, IEEE Trans. Automat. Contr., vol. AC-39, 1994, pp. 2484–2488.MATHCrossRefGoogle Scholar
  96. 44.
    De Oliveita, M. C., J. C. Geromel and J. Bernussou, Extended \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Norm Characterizations and Controller Parameterizations for Discrete-Time Systems, Int. J. Contr., vol. 75, 2002, pp. 666–679.CrossRefGoogle Scholar
  97. 212.
    Mahmoud, M. S., Robust Stability and Stabilization of a Class of Nonlinear Systems with Delays, J. Math. Probl. Eng., vol. 4, no. 2, 1998, pp. 165–185.MATHCrossRefGoogle Scholar
  98. 93.
    Geromel, J. C., M. C. D. Olivera and J. Bernussou, Robust Filtering of Discrete-Time Linear Systems with Parameter Dependent Lyapounov Functions, SIAM J. Contr. Optim., vol. 41, 2002, pp. 700–711.MATHGoogle Scholar
  99. 118.
    Hassibi, A. and S. Boyd, Quadratic Stabilization and Control of Piecewise-Linear Systems, Proceedings of American Control Conference (ACC), Philadelphia, PA, 1998, pp. 3659–3664.Google Scholar
  100. 215.
    Mahmoud, M. S., Robust \(\mathcal{H}_{\infty}\) Control of Discrete Systems with Uncertain Parameters and Unknown Delays, Automatica, vol. 36, 2000, pp. 627–635.MATHCrossRefGoogle Scholar
  101. 103.
    Gu, K. Q. and S. I. Niculescu, Additional Dynamics in Transformed Time-Delay Systems, IEEE Trans. Automat. Contr., vol. 45, 2000, pp. 572–575.MathSciNetMATHCrossRefGoogle Scholar
  102. 120.
    He, Y., M. Wu and Q. L. Han, Delay-Dependent \(\mathcal{H}_{\infty}\) Control of Linear Discrete-Time Systems with an Interval-Like Time-Varying Delay, Int. J. Syst. Sci., vol. 39, no. 3, 2008, pp. 427–436.MathSciNetMATHCrossRefGoogle Scholar
  103. 56.
    El-Fara, N. H., P. Mhaskar and P. D. Christofides, Output Feedback Control of Switched Nonlinear Systems using Multiple Lyapunov Functions, Syst. Contr. Lett., vol. 54, 2005, pp. 1163–1162.CrossRefGoogle Scholar
  104. 136.
    Hespanha, J. P., D. Liberzon, D. Angeli and E. D. Sontag, Nonlinear Norm-Observability Notions and Stability of Switched Systems, IEEE Trans. Automat. Contr., vol. 52, no. 2, 2007, pp. 154–168.MathSciNetGoogle Scholar
  105. 245.
    Mahmoud, M. S. and N. F. Al-Muthairi, Quadratic Stabilization of Continuous-Time Systems with State Delay and Norm-Bounded Time Varying Uncertainties, IEEE Trans. Automat. Contr., vol. AC-39, 1994, pp. 2135–2139.MathSciNetMATHCrossRefGoogle Scholar
  106. 211.
    Mahmoud, M. S., Robust Stability and Stabilization of a Class of Uncertain Nonlinear Systems with Delays, J. Math. Probl. Eng., vol. 3, 1997, pp. 1–21.Google Scholar
  107. 145.
    Ismail, A. and M. S. Mahmoud, A Descriptor Approach to Simultaneous \(\mathcal{H}_{2}/\mathcal{H}_{\infty}\) Control of Jumping Time-delay Systems., IMA J. Math Control and Info., vol. 21, 2004, 95–114.MathSciNetMATHCrossRefGoogle Scholar
  108. 114.
    Han, Q. L., On Robust Stability of Neutral Systems with Time-Varying Discrete Delay and Norm-Bounded Uncertainty, Automatica, vol. 40, no. 6, 2004, pp. 1087–1092.MathSciNetMATHCrossRefGoogle Scholar
  109. 86.
    Germani, A., C. Manes and P. Palumbo, Filtering of Switching Systems via a Singular Minimax Approach, Proceeding of the 41th IEEE Conference on Decision and Control, Las Vegas, NV, December 2002.Google Scholar
  110. 16.
    Bernstein, D. S. and W. M. Haddad, Steady-State Kalman Filtering with an \(\mathcal{H}_{\infty}\) Error Bound, Syst. Contr. Lett., vol. 16, 1991, pp. 309–317.MathSciNetCrossRefGoogle Scholar
  111. 393.
    Wu, L., P. Shi, C. Wang and H. Gao, Delay-Dependent Robust \(\mathcal{H}_{\infty}\) and \(\mathcal{L}_{2}-\mathcal{H}_{\infty}\) Filtering for LPV Systems with Both Discrete and Distributed Delays, IEE Proc. Contr. Theory Appl., vol. 153, 2006, pp. 483–492.MathSciNetCrossRefGoogle Scholar
  112. 163.
    Kharitonov, V. L. and D. Melchor-Aguilar, On Delay-Dependent Stability Conditions for Time-varying Systems, Syst. Contr. Lett., vol. 46, 2000, pp. 173–180.MathSciNetCrossRefGoogle Scholar
  113. 264.
    Mahmoud, M. S. and M. Zribi, Robust and \(\mathcal{H}_{\infty}\) Stabilization of Interconnected Systems with Delays, IEE Proc.-Contr. Theory Appl., vol. 145, 1998, pp. 558–567.Google Scholar
  114. 91.
    Geromel, J. C., J. Bernussou and M. C. de Oliveira, \(\mathcal{H}_{2}\) Norm Optimization with Constrained Dynamic Output Feedback Controllers: Decentralized and Reliable Control, IEEE Trans. Automat. Contr., vol. 44, 1999, pp. 1449–1454.MathSciNetMATHCrossRefGoogle Scholar
  115. 408.
    Xu, H., Y. Zou and S. Xu, Robust \(\mathcal{H}_{\infty}\) Control for a Class of Uncertain Nonlinear Two-Dimensional Systems, Int. J. Innovative Comput. Inf. Contr., vol. 1, no. 2, 2005, pp. 181–191.MathSciNetGoogle Scholar
  116. 447.
    Zhu, Y., D. Q. Li and G. Feng, \(\mathcal{H}_{\infty}\) Controller Synthesis of Uncertain Piecewise Continuous-Time Linear Systems, IEE Proc.-Contr. Theory Appl., vol. 152, 2005, pp. 513–519.CrossRefGoogle Scholar
  117. 94.
    Geromel, J. C., P. L. D. Peres and S. R. de Souza, A Convex Approach to the Mixed \(\mathcal{H}_{2}/\mathcal{H}_{\infty}\) Control Problem for Discrete-Time Uncertain Systems, SIAM J. Contr. Optim., vol. 33, 1995, pp. 1816–1833.MathSciNetMATHCrossRefGoogle Scholar
  118. 368.
    Sun, Y. G., L. Wang and G. Xie, Delay-Dependent Robust Stability and \(\mathcal{H}_{\infty}\) Control for Uncertain Discrete-Time Switched Systems with Mode-Dependent Time-Delays, Appl. Math. Comput., vol. 180, 2006, pp. 428–435.MathSciNetMATHCrossRefGoogle Scholar
  119. 134.
    Hespanha, J. P. and A. S. Morse, Stability of Switched Systems with Average Dwell-Time, Proceedings of the 38th IEEE Conference on Decision Control, Sydney, 1999, pp. 2655–2660.Google Scholar
  120. 96.
    Gorecki, H., S. Fuska, P. Garbowski and A. Korytowski, Analysis and Synthesis of Time-Delay Systems, Wiley, New York, NY, 1989.MATHGoogle Scholar
  121. 317.
    Palhares, R. M. and P. L. D. Peres, Robust \(\mathcal{H}_{\infty}\) Filtering Design with Pole Placement Constraint via LMIs, J. Optim. Theory Appl., vol. 102, 1999, pp. 239–261.MathSciNetMATHCrossRefGoogle Scholar
  122. 256.
    Mahmoud, M. S. and P. Shi, Robust Kalman Filtering for Continuous Time-Lag Systems with Jump Parameters, IEEE Trans. Circuits Syst.-I, vol. 50, no. 1, 2003, pp. 98–105.MathSciNetCrossRefGoogle Scholar
  123. 266.
    Mahmoud, M. S. and M. Zribi, Output Feedback Design for Uncertain Systems with Delays, IMA J. Math Contr. Inf., vol. 19, 2002, pp. 297–312.MathSciNetMATHCrossRefGoogle Scholar
  124. 220.
    Mahmoud, M. S., Uncertain Jumping Systems with Strong and Weak Functional Delays, Automatica, vol. 40, 2004, pp. 501–510.MATHCrossRefGoogle Scholar
  125. 210.
    Mahmoud, M. S., Robust Performance Results for Discrete-Time Systems, J. Math. Probl. Eng. Syst., vol. 4, 1997, pp. 17–38.Google Scholar
  126. 195.
    Lin, H. and P. J. Antsaklis, Hybrid State Feedback Stabilization with \(\ell_{2}\) Performance for Discrete-Time Switched Linear Systems, Int. J. Contr., vol. 81, 2008, pp. 1114–1124.MathSciNetMATHCrossRefGoogle Scholar
  127. 254.
    Mahmoud, M. S. and S. J. Saleh, Regulation of Water Quality Standards in Streams by Decentralized Control, Int. J. Contr., vol. 41, 1985, pp. 525–540.MathSciNetMATHCrossRefGoogle Scholar
  128. 189.
    Li, H. and M. Fu, A Linear Matrix Inequality Approach to Robust \(\mathcal{H}_{\infty}\) Filtering, IEEE Trans. Signal Process., vol. 47, 1997, pp. 2338–2350.Google Scholar
  129. 293.
    Mignone, D. G. F. Trecate and M. Morari, Stability and Stabilization of Piecewise Affine and Hybrid Systems: An LMI Approach, Proceedings of the 39th IEEE CDC, Sydney, Australia, 2000, pp. 504–509.Google Scholar
  130. 82.
    Gao, H. and T. Chen, New Results on Stability of Discrete-Time Systems with Time-Varying State-Delay, IEEE Trans. Automat. Contr., vol. 52, no. 2, 2007, pp. 328–334.MathSciNetCrossRefGoogle Scholar
  131. 182.
    Lehman, B., J. Bentsman, S. V. Lunel and E. I. Verriest, Vibrational Control of Nonlinear Time-Lag Systems with Bounded Delay: Averaging Theory, Stability and Transient Behavior, IEEE Trans. Automat. Contr., vol. 39, no. 5, 1994, pp. 898–912.MATHCrossRefGoogle Scholar
  132. 154.
    Jiang, B., M. Staroswiecki and V. Cocquempot, \(\mathcal{H}_{\infty}\) Fault Detection Filter Design for Linear Discrete-Time Systems with Multiple Time-Delays, Int. J. Syst. Sci., vol. 34, no. 5, 2003, pp. 365–373.MathSciNetMATHCrossRefGoogle Scholar
  133. 111.
    Han, Q.-L., A Descriptor System Approach to Robust Stability of Uncertain Neutral Systems with Discrete and Distributed Delays, Automatica, vol. 40, 2004, 1791–1796.MATHCrossRefGoogle Scholar
  134. 236.
    Mahmoud, M. S. and Abdulla Ismail, Passivity Analysis and Synthesis of Discrete-Time Delay Systems, J. Dyn. Continuous, Disc. Impulsive Syst., Series A, vol. 11, no. 4, 2004, pp. 525–544.MATHGoogle Scholar
  135. 105.
    Gu, K., V. L. Kharitonov and J. Chen, Stability of Time-Delay Systems, Birkhauser, Boston, MA, 2003.MATHCrossRefGoogle Scholar
  136. 198.
    Lin, Q., G. Wang and T. H. Lee, A Less Conservative Robust Stability Test for Linear Uncertain Time-Delay Systems, IEEE Trans. Automat. Contr., vol. 51, 2006, pp. 87–91.MathSciNetCrossRefGoogle Scholar
  137. 138.
    Hetel, L., J. Daafouz and C. Iung, Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays, IEEE Trans. Automat. Contr., vol. 51, no. 10, 2006, pp. 1668–1674.MathSciNetCrossRefGoogle Scholar
  138. 109.
    Hale, J., Theory of Functional Differential Equations, Springer, New York, NY, 1977.MATHCrossRefGoogle Scholar
  139. 167.
    Kharitonov, V. L. and A. P. Zhabko, Lyapunov-Krasovskii Approach to the Robust Stability Analysis of Time-Delay Systems, Automatica, vol. 39, 2003, pp. 15–20.MathSciNetMATHCrossRefGoogle Scholar
  140. 199.
    Liu, X. P., Output Regulation of Strongly Coupled Symmetric Composite Systems, Automatica, vol. 28, 1992, pp. 1037–1041.MATHCrossRefGoogle Scholar
  141. 79.
    Gao, H. and C. Wang, A Delay-Dependent Approach to Robust \(\mathcal{H}_{\infty}\) and \({L}_{2}-{L}_{\infty}\) Filtering for a Class of Uncertain Nonlinear Time-Delayed Systems, IEEE Trans. Automat. Contr., vol. 48, no. 9, 2003, pp. 1661–1666.CrossRefGoogle Scholar
  142. 186.
    Leith, D. J., R. N. Shorten, W. E. Leithead, O. Mason and P. Curran, Issues in the Design of Switched Linear Control Systems: A Benchmark Study, Int. J. Adaptive Contr. Signal Process., vol. 17, no. 2, 2003, pp. 103–118.MATHCrossRefGoogle Scholar
  143. 352.
    Siouris, G., An Engineering Approach to Optimal Control and Estimation Theory, Wiley, New York, NY, 1996.Google Scholar
  144. 126.
    He, Y., M. Wu, G. P. Liu and J. H. She, Output Feedback Stabilization for a Discrete-Time System with a Time-Varying Delay, IEEE Trans. Automat. Contr., vol. 53, no. 10, 2008, pp. 2372–2377.MathSciNetCrossRefGoogle Scholar
  145. 191.
    Li, Z., C. Wen, Y. C. Soh and W. Xie, Generalized Matrix Measure of Switched Nonlinear Systems, IEEE Trans. Automat. Contr., vol. 47, 2002, pp. 178–183.MathSciNetCrossRefGoogle Scholar
  146. 132.
    Hespanha, J. P., Modeling and Analysis of Stochastic Hybrid Systems, IEE Proc.-Contr. Theory Appl., vol. 153, 2006, pp. 520–535.MathSciNetCrossRefGoogle Scholar
  147. 170.
    Kim, D. K., P. G. Park and J. W. Ko, Output Feedback \(\mathcal{H}_{\infty}\) Control of Systems Over Communication Networks using a Deterministic Switching Systems Approach, Automatica, vol. 40, no. 3, 2004, pp. 1205–1212.MathSciNetMATHCrossRefGoogle Scholar
  148. 420.
    Yuan, K., J. Cao and H. X. Li, Robust Stability of Switched Cohen-Grossberg Neural Networks with Mixed Time-Varying Delays, IEEE Trans. Syst. Man Cybern.-Part B, vol. 36, 2006, pp. 1356–1363.CrossRefGoogle Scholar
  149. 127.
    He, Y., M. Wu, J. H. She and G. P. Liu, Delay-Dependent Robust Stability Criteria for Uncertain Neutral Systems with Mixed Delays, Syst. Contr. Lett., vol. 51, no. 1, 2004, pp. 57–65.MathSciNetMATHCrossRefGoogle Scholar
  150. 279.
    Mahmoud, M. S., M. N. Nounou and H. N. Nounou, Analysis and Synthesis of Uncertain Switched Discrete-Time Systems, IMA J. Math. Contr. Inf., vol. 24, 2007, pp. 245–257.MathSciNetMATHCrossRefGoogle Scholar
  151. 381.
    Wang, Z. and F. Yang, Robust Filtering for Uncertain Linear Systems with Delayed States and Outputs, IEEE Trans. Circuits Syst. I, vol. 49, 2002, pp. 125–130.CrossRefGoogle Scholar
  152. 158.
    Kalman, R. E., A New Approach to Linear Filtering and Prediction Problems, Trans. ASME-J. Basic Eng., vol. 82, 1960, pp. 35–45.CrossRefGoogle Scholar
  153. 213.
    Mahmoud, M. S., Robust \(\mathcal{H}_{\infty}\) Control of Discrete Systems with Uncertain Parameters and Unknown Delays, Automatica, vol. 36, 2000, pp. 627–635.MATHCrossRefGoogle Scholar
  154. 204.
    Mahmoud, M. S., Output Feedback stabilization of Uncertain Systems with State Delay, in Analysis and Synthesis Techniques in Complex Control and Dynamic Systems, vol. 63, Leondes, C. T. (Editor), Academic, New York, NY, 1994, pp. 197–257.Google Scholar
  155. 148.
    Ji, Z. and L. Wang, Robust \(\mathcal{H}_{\infty}\) Control and Quadratic Stabilization of Uncertain Switched Linear Systems, Proceedings of the American Control Conference, Portland, OR, 2004, pp. 4543–4548.Google Scholar
  156. 119.
    Hattingh, J. and M. Claassen, SecuringWater Quality for Life, Int. J. Water Resour. Dev., vol. 24, 2008, pp. 401–405.CrossRefGoogle Scholar
  157. 184.
    Leite, V. J. S. and P. L. D. Peres, Robust ontrol Through Piecewise Lyapunov Functions for Discrete Time-Varying Uncertain Systems, Int. J. Contr., vol. 77, 2004, pp. 230–238.MathSciNetMATHCrossRefGoogle Scholar
  158. 244.
    Mahmoud, M. S. and N. F. Al-Muthairi, Design of Robust Controllers for Time-Delay Systems, IEEE Trans. Automat. Contr., vol. AC-39, 1994, pp. 995–999.MathSciNetMATHCrossRefGoogle Scholar
  159. 61.
    Feng, G., Observer-Based Output Feedback Controller Design of Piecewise Discrete-Time Linear Systems, IEEE Trans. Circuits Syst.-I, vol. 50, 2003, pp. 448–451.CrossRefGoogle Scholar
  160. 153.
    Jiang, X., Q.-L. Han and X. Yu, Stability Criteria for Linear Discrete-Time Systems with Interval-Like Time-varying Delay, Proceedings of the American Control Conference, Portland, OR, 2005, pp. 2817–2822.Google Scholar
  161. 277.
    Mahmoud, M. S., M. F. Hassan and S. J. Saleh, Decentralized Structures for Stream Water Quality Control Problems, Optimal Contr. Appl. Methods, vol. 6, 1987, pp. 167–186.CrossRefGoogle Scholar
  162. 187.
    Leonessa, A., W. M. Haddad and V.-S. Chellaboina, Hierarchical Nonlinear Switching Control Design with Applications to Propulsion Systems, Springer, London, 2000.MATHGoogle Scholar
  163. 334.
    Pettit, N. B. L. and P. E. Wellstead, Analysing Piecewise Linear Dynamical Systems, IEEE Contr. Syst. Mag., vol. 15, 1995, pp. 43–50.CrossRefGoogle Scholar
  164. 217.
    Mahmoud, M. S., Robust Stability and \(\mathcal{H}_{\infty}\) Estimation for Uncertain Discrete Systems with State-Delay, J. Math. Probl. Eng., vol. 7, no. 5, 2001, pp. 393–412.MATHCrossRefGoogle Scholar
  165. 177.
    Kwon, W. H., J. W. Kang, Y. S. Lee and Y. S. Moon, A Simple Receding Horizon Control for State Delayed Systems and its Stability Criterion, J. Process. Contr., vol. 13, 2003, pp. 539–551.CrossRefGoogle Scholar
  166. 146.
    Ivanescu, D., J. M. Dion, L. Dugard and S. I. Niculescu, .Dynamical Compensation for Time-Delay Systems: An LMI Approach, Int. J. Robust Nonlinear Contr., vol. 10, 2000, pp. 611–628.MathSciNetMATHCrossRefGoogle Scholar
  167. 141.
    Hovd, M. and S. Skogestad, Control of Symmetrically Interconnected Plants, Automatica, vol. 30, 1994, pp. 957–973.MathSciNetMATHCrossRefGoogle Scholar
  168. 37.
    Cheng, C. J., T. L. Liao, J. J. Yan and C. C. Hwang, Exponential Synchronization of a Class of Neural Networks with Time-Varying Delays, IEEE Trans. Syst. Man Cybern.-Part B, vol. 36, 2006, pp. 209–215.CrossRefGoogle Scholar
  169. 166.
    Kharitonov, V. L. and S. I. Niculescu, On the Stability of Linear Systems with Uncertain Delay, IEEE Trans. Automat. Contr., vol. 48, no. 1, 2003, pp. 127–132.MathSciNetCrossRefGoogle Scholar
  170. 202.
    Liu, X. G., R. R. Martin, M. Wu and M. L. Tang, Delay-Dependent Robust Stabilization of Discrete-Time Systems with Time-Varying Delays, IEE Proc. Contr. Theory Appl., vol. 153, no. 6, 2006, pp. 689–702.MathSciNetCrossRefGoogle Scholar
  171. 183.
    Leite, V. J. and M. F. Miranda, Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach, Math Probl. Eng., 2008, vol. 2008, pp. 1–15.MathSciNetCrossRefGoogle Scholar
  172. 74.
    Gahinet, P., A. Nemirovski, A. L. Laub and M. Chilali, LMI Control Toolbox, The Math Works, Boston, MA, 1995.Google Scholar
  173. 394.
    Xie, L. H., Output Feedback \(\mathcal{H}_{\infty}\) Control of Systems with Parameter Uncertainty’. Int. J. Contr., vol. 63, 1996, pp. 741–750.MATHCrossRefGoogle Scholar
  174. 76.
    Gao, F., S. Zhong and X. Gao, Delay-Dependent Stability of a Type of Linear Switching Systems with Discrete and Distributed Time-Delays, Appl. Math Comput., vol. 196, 2008, pp. 24–39.MathSciNetMATHCrossRefGoogle Scholar
  175. 156.
    Johansson, M. and A. Rantzer, Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems’, IEEE Trans. Automat. Contr., vol. 43, no. 4, 1998, pp. 555–559.MathSciNetMATHCrossRefGoogle Scholar
  176. 52.
    Du, D., S. Zhou and B. Zhang, Oliveita, Generalized H2 Output Feedback Controller Design for Uncertain Discrete-Time hybrid Systems via Switched Lyapunov Functions, Nonlinear Anal., vol. 65, 2006, pp. 2135–2146.MathSciNetMATHCrossRefGoogle Scholar
  177. 269.
    Mahmoud, M. S., N. F. Al-Muthairi and S. Bingulac, Robust Kalman Filtering for Continuous Time-Lag Systems, Syst. Contr. Lett., vol. 38, no. 4, 1999, pp. 309–319.MathSciNetMATHCrossRefGoogle Scholar
  178. 267.
    Mahmoud, M. S. and M. Zribi, Robust Output Feedback Control for Nonlinear Systems Including Actuators, J. Syst. Anal. Model. Simulat., vol. 43, no. 6, June 2003, pp. 771–792.MathSciNetMATHCrossRefGoogle Scholar
  179. 208.
    Mahmoud, M. S., Design of Stabilizing Controllers for Uncertain Discrete-Time Systems with State-Delay, Syst. Anal. Model. Simulat., vol. 21, 1995, pp. 13–27.MATHGoogle Scholar
  180. 125.
    He, Y., M. Wu, G. P. Liu and J. H. She, Output Feedback Stabilization for Discrete-Time Systems with a Time-Varying Delay, Proceedings of the 26th Chinese Control Conference, China, 2007, pp. 64–70.Google Scholar
  181. 116.
    Han, W., Stability of Motion, Springer, New York, NY, 1967.Google Scholar
  182. 121.
    He, Y., M. Wu and J. H. She, Delay-Dependent Stability Criteria for Linear Systems with Multiple Time-Delays, IEE Proc.- Contr. Theory Appl., vol. 153, no. 4, 2006, pp. 447–452.MathSciNetCrossRefGoogle Scholar
  183. 142.
    Hu, Z., Decentralized Stabilization of Large-Scale Interconnected Systems with Delays, IEEE Trans. Automat. Contr., vol. 39, no. 5, 1994, pp. 180–182.MATHGoogle Scholar
  184. 196.
    Lin, H. and P. J. Antsaklis, Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results, IEEE Trans. Automat. Contr., vol. 54, 2009, pp. 308–322.MathSciNetCrossRefGoogle Scholar
  185. 347.
    Shi, P., M. Mahmoud and S. Nguang, Robust Filtering for Jumping Systems with Mode-Dependent Delays, Signal Process., vol. 86, 2006, pp. 140–152.MATHCrossRefGoogle Scholar
  186. 92.
    Geromel, J. C., P. Colaneri and P. Bolzern, Dynamic Output Feedback Control of Switched Linear Systems, IEEE Trans. Automat. Contr., vol. 53, no. 4, 2008, pp. 720–733.MathSciNetCrossRefGoogle Scholar
  187. 137.
    Hespanha, J. P., P. Naghshtabrizi and Y. Xu, A Survey of Recent Results in Networked Control Systems, Proc. IEEE, vol. 95, no. 1, 2007, pp. 138–162.CrossRefGoogle Scholar
  188. 262.
    Mahmoud, M. S. and L. Xie, Guaranteed Cost Control of Uncertain Discrete Systems with Delays, Int. J. Contr., vol. 73, no. 2, 2000, pp. 105–114.MathSciNetMATHCrossRefGoogle Scholar
  189. 188.
    Li, X. and C. de Souza, Criteria for Robust Stability and Stabilization of Test for Uncertain Linear Systems with State-Delay, Automatica, vol. 33, 1997, pp. 1657–1662.CrossRefGoogle Scholar
  190. 257.
    Mahmoud, M. S. and P. Shi, Robust Stability, Stabilization and \(\mathcal{H}_{\infty}\) Control of Time-Delay Systems with Markovian Jump Parameters, Int. J. Robust Nonlinear Contr., vol. 13, 2003, pp. 755–784.MathSciNetMATHCrossRefGoogle Scholar
  191. 130.
    Hein, Y., Q. P. Ha and V. N. Phat, Stability and Stabilization of Switched Linear Dynamic Systems with Time Delay and Uncertainties, Appl. Math Comput., vol. 210, no. 1, 2009, pp. 223–231.MathSciNetCrossRefGoogle Scholar
  192. 140.
    Hlava, J., Time Delay Systems Applications in Textile Industry – Modeling of Sliver Drafting Process, Time Delay Systems 2003 – A Proceedings Volume from the 4th IFAC Workshop, Elsevier, Oxford, 2003, pp. 287–292.Google Scholar
  193. 221.
    Mahmoud, M. S., Resilient Control of Uncertain Dynamical Systems, Springer, Berlin, 2004.MATHCrossRefGoogle Scholar
  194. 30.
    Cao, Y. and P. M. Frank, Robust \(\mathcal{H}_{\infty}\) Disturbance Attenuation for a Class of Uncertain Discrete-Time Fuzzy Systems, IEEE Trans. Fuzzy Syst., vol. 8, 2000, pp. 406–415.CrossRefGoogle Scholar
  195. 69.
    Fridman, E. and U. Shaked, An Improved Delay-Dependent \(\mathcal{H}_{\infty}\) Filtering of Linear Neutral Systems, IEEE Trans. Signal Process., vol. 42, 2004, pp. 668–673.MathSciNetCrossRefGoogle Scholar
  196. 102.
    Gu, K., Survey on Recent Results in the Stability and Control of Time Delay Systems, J. Dyn. Syst., Meas. Contr., vol. 125, 2005, pp. 158–165.CrossRefGoogle Scholar
  197. 112.
    Han, Q.-L., New Results for Delay-Dependent Stability of Linear Systems with Timevarying Delay, Int. J. Syst. Sci., vol. 33, 2003, pp. 213–228.CrossRefGoogle Scholar
  198. 143.
    Huang, S., J. Lam, G. H. Yang and S. Zhang, Fault Tolerant Decentralized \(\mathcal{H}_{\infty}\) Control for Symmetric Composite Systems, IEEE Trans. Automat. Contr., vol. 44, 1999, pp. 2108–2114.MathSciNetMATHCrossRefGoogle Scholar
  199. 181.
    Lee, Y. S., Y. S. Moon, W. H. Kwon and P. G. Park, Delay-Dependent \(\mathcal{H}_{\infty}\) Control for Uncertain Systems with a State-Delay, Automatica, vol. 40, 2004, pp. 65–72.MathSciNetMATHCrossRefGoogle Scholar
  200. 216.
    Mahmoud, M. S., Robust Control and Filtering for Time-Delay Systems, Marcel-Dekker, New-York, NY, 2000.MATHGoogle Scholar
  201. 129.
    Heemels, W. P. M. H., De Schutter, B. and A. Bemporad, On The Equivalence of Classes of Hybrid Systems: Mixed Logical Dynamical and Complimentarily Systems, Automatica, vol. 37, no. 7, 2001, pp. 1085–1091.MATHCrossRefGoogle Scholar
  202. 249.
    Mahmoud, M. S. and S. Bingulac, Robust Design of Stabilizing Controllers for Interconnected Time-Delay Systems, Automatica, vol. 34, 1998, pp. 795–800.MathSciNetMATHCrossRefGoogle Scholar
  203. 90.
    Geromel, J. C. and P. Colaneri, Stability and Stabilization of Discrete-Time Switched Linear Systems, Int. J. Contr., vol. 79, no. 7, 2006, pp. 719–728.MathSciNetMATHCrossRefGoogle Scholar
  204. 372.
    Sun, X. M., W. Wang, G. P. Liu and J. Zhao, Stability Analysis for Linear Switched Systems with Time-Varying Delays, IEEE Trans. Syst. Man Cybern.-Part B, vol. 38, 2008, pp. 528–533.Google Scholar
  205. 35.
    Cheng, C. J., J. J. Yan and C. C. Hwang, Globally Asymptotic Stability of a Class of Neutral-Type Neural Networks with Delays, IEEE Trans. Syst. Man Cybern.-Part B, vol. 36, 2006, pp. 1191–1195.CrossRefGoogle Scholar
  206. 180.
    Lee, T. N. and U. L. Radovic, Decentralized Stabilization of Linear Continuous or Discrete-Time Systems with Delays in the Interconnection, IEEE Trans. Automat. Contr., vol. 33, no. 5, 1989, pp. 757–760.MathSciNetGoogle Scholar
  207. 95.
    Goebel, R., R. G. Sanfelice and A. R. Teel, Hybrid Dynamical Systems, IEEE Contr. Syst. Mag., vol. 9, 2009, pp. 28–93.MathSciNetGoogle Scholar
  208. 144.
    Imura, J. I. and A. Van der Schaft, Characterization of Well-Posedness of Piecewise-Linear Systems, IEEE Trans. Automat. Contr., vol. 45, 2000, pp. 1600–1619.MATHCrossRefGoogle Scholar
  209. 190.
    Li, C., H. Wang and X. Liao, Delay-Dependent Robust Stability of Uncertain Fuzzy Systems with Time-Varying Delays, IEE Proc. Contr. Theory Appl., vol. 151, 2004, pp. 417–421.CrossRefGoogle Scholar
  210. 113.
    Han, K. H., S. Kim, Y. J. Kim and J. H. Kim, Internet Control Architecture for Internetbased Personal Robot, Autonomous Robots, vol. 10, 2001, pp. 135–147.MATHCrossRefGoogle Scholar
  211. 354.
    Song, S. H. and J. K. Kim, \(\mathcal{H}_{\infty}\) Control of Discrete-Time Linear Systems with Norm-Bounded Uncertainties and Time-Delay in State, Automatica, vol. 34, 1998, pp. 137–139.MathSciNetMATHCrossRefGoogle Scholar
  212. 258.
    Mahmoud, M. S. and P. Shi, Optimal Guaranteed Cost Filtering for Markovian Jump Discrete-Time Systems, Math. Probl. Eng., vol. 12, no. 1, 2004, pp. 33–48.MathSciNetCrossRefGoogle Scholar
  213. 178.
    Lee, K. H., Robust Decentralized Stabilization of a Class of Linear Discrete-Time Systems with Nonlinear Interactions, Int. J. Contr., vol. 80, 2007, pp. 1544–1551.MATHCrossRefGoogle Scholar
  214. 133.
    Hespanha, J. P., Uniform Stability of Switched Linear Systems: Extensions of Lasalles Invariance Principle, IEEE Trans. Automat. Contr., vol. 49, no. 4, 2004, pp. 470–482.MathSciNetCrossRefGoogle Scholar
  215. 172.
    Kolmanovskii, V. B. and J. P. Richard, Stability of Some Linear Systems with Delays, IEEE Trans. Automat. Contr., vol. 44, 1999, pp. 984–989.MathSciNetMATHCrossRefGoogle Scholar
  216. 444.
    Zhou, S. and J. Lam, Robust Stabilization of Delayed Singular Systems with Linear Fractional Parametric Uncertainties, Circuits Syst. Signal Process., vol. 22, no. 6, 2003, pp. 579–588.MathSciNetMATHCrossRefGoogle Scholar
  217. 168.
    Kim, J. H., Delay and its Time-Derivative Dependent Robust Stability of Time-Delayed Linear Systems with Uncertainty, IEEE Trans. Automat. Contr., vol. 46, no. 5, 2001, pp. 789–792.MATHCrossRefGoogle Scholar
  218. 106.
    Guo, L., \(\mathcal{H}_{\infty}\) Output Feedback Control for Delay Systems with Nonlinear and Parametric Uncertainties, IEE Proc. Contr. Theory Appl., vol. 49, 2002, pp. 226–236.Google Scholar
  219. 150.
    Ji, Z., L. Wang and G. Xie, Quadratic Stabilization of Switched Systems, Int. J. Syst. Sci., vol. 36, no. 6, 2005, pp. 395–404.MathSciNetMATHCrossRefGoogle Scholar
  220. 345.
    Shi, P., E. K. Boukas and R. K. Agarwal, Optimal Guaranteed Cost Control of Uncertain Discrete Time-Delay Systems, J. Comput. Appl. Math., vol. 157, 2003, pp. 435–451.MathSciNetMATHCrossRefGoogle Scholar
  221. 57.
    Elsayed, A. and M. Grimble, A new approach to \(\mathcal{H}_{\infty}\) design for optimal digital linear filters, IMA J. Math. Contr. Inf., vol. 6, no. 3, 1989, pp. 233–251.MathSciNetMATHCrossRefGoogle Scholar
  222. 373.
    Suplin, V., E. Fridman and U. Shaked, \(\mathcal{H}_{\infty}\) Control of Linear Uncertain Time-Delay Systems-A Projection Approach, IEEE Trans. Automat. Contr., vol. 51, 2006, pp. 680–685.MathSciNetCrossRefGoogle Scholar
  223. 377.
    Tshii, H. and B. A. Francis, Stabilizing a Linear System by Switching Control with Dwell Time, IEEE Trans. Automat. Contr., vol. 47, no. 2, 2002, pp. 1962–1973.CrossRefGoogle Scholar
  224. 164.
    Kharitonov, V. L. and D. Melchor-Aguilar, Additional Dynamics for General Class of Time-delay Systems, IEEE Trans. on Automat. Contr., vol. 48, 2003, pp. 1060–1064.MathSciNetCrossRefGoogle Scholar
  225. 203.
    Lozano, R., B. Brogliato, O. Egeland and B. Maschke, Dissipative Systems Analysis and Control: Theory and Applications, Springer, London, 2000.MATHGoogle Scholar
  226. 174.
    Koutsoukos, X. D. and P. J. Antsaklis, Design of Stabilizing Switching Control Laws for Discrete- and Continuous-Time Linear Systems Using Piecewise-Linear Lyapunov Functions, Int. J. Contr., vol. 75, 2002, pp. 932–945.MathSciNetMATHCrossRefGoogle Scholar
  227. 395.
    Xie, G. and L. Wang, Quadratic Stability and Stabilization of Discrete-Time Switched Systems with State-Delay, Proceedings of the 43rd Conference on Decision Control, Atlantis, Paradise Island, Bahamas, December 14–17, 2004, pp. 3235–3240.Google Scholar
  228. 115.
    Han, Q.-L., Stability Criteria for a Class of Linear Neutral Systems with Time-varying Discrete and Distributed Delays, IMA J. Math Contr. Inf., vol. 20, 2003, pp. 371–386.MATHCrossRefGoogle Scholar
  229. 439.
    Zhang, L., P. Shi, C. Wang and H. J. Gao, Robust \(\mathcal{H}_{\infty}\) Filtering for Switched Linear Discrete-Time Systems with Polytopic Uncertainties, Int. J. Adapt. Contr. Signal Process., vol. 20, 2006, pp. 291–304.MathSciNetMATHCrossRefGoogle Scholar
  230. 135.
    Hespanha, J. P. and A. S. Morse, Switching Between Stabilizing Controllers, Automatica, vol. 38, 2002, pp. 1905–1917.MathSciNetMATHCrossRefGoogle Scholar
  231. 209.
    Mahmoud, M. S., Dynamic Control of Systems with Variable State-Delays, Int. J. Robust Nonlinear Contr., vol. 6, 1996, pp. 123–146.MATHCrossRefGoogle Scholar
  232. 149.
    Ji, Z. and L. Wang, Robust Stability and Stabilization of a Class of Nonlinear Switched Systems, Proceedings of the IASTED Conference on Modeling, Identification, and Control, Lanzarote, Spain, 2006, pp. 37–42.Google Scholar
  233. 17.
    Bingulac, S. and H. F. VanLandingham, Algorithms for Computer-Aided Design of Multivariable Control Systems, Marcel-Dekker, New York, NY, 1993.MATHGoogle Scholar
  234. 336.
    Rantzer, A. and M. Johansson, Piecewise Linear Quadratic Optimal Control, IEEE Trans. Automat. Contr., vol. 45, 2000, pp. 629–637.MathSciNetMATHCrossRefGoogle Scholar

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© Springer US 2010

Authors and Affiliations

  1. 1.Department of Systems EngineeringKing Fahd University of Petroleum and Minerals (KFUPM)DhahranSaudi Arabia

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