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Applications to Water-Quality Control

  • Magdi S. Mahmoud
Chapter

Abstract

Switched systems have been intensively studied in recent years due to their widespread applications, including power systems and chemical processes [41] and mechanical systems [47]. A wide class of switched systems composed of a finite family of continuous- or discrete-time subsystems (called modes) and a rule that governs the switching between these subsystems. Each mode is regarded as a state of a finite-state machine whose evolution dynamics determines the switching. In this work, we consider that the modes are represented by discrete-time linear systems with unknown-but-bounded delays. Research investigations into problems pertaining to switched dynamical systems have received a great deal of attention because of the fast development in computing technologies [15, 28, 42, 47, 174, 193] and the references cited therein.

Keywords

Linear Matrix Inequality Biochemical Oxygen Demand Output Feedback Static Output Feedback Arbitrary Switching 
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. 225.
    Mahmoud, M. S., Delay-Dependent \(\mathcal{H}_{2}\) Filtering of a Class of Switched Discrete-Time State-Delay Systems, J. Signal Process., vol. 88, no. 11, 2008, pp. 2709–2719.MATHCrossRefGoogle Scholar
  2. 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
  3. 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
  4. 224.
    Mahmoud, M. S., Linear Hybrid Systems with Time-Varying Delays: \(\mathcal{H}_{\infty}\) Stabilization Schemes, Int. J. Syst. Contr. Commun., vol. 1, no. 2, 2008, pp. 147–169.CrossRefGoogle Scholar
  5. 25.
    Boukas, E. K. and M. S. Mahmoud, A Practical Approach to Control of Nonlinear Discrete-Time State-Delay Systems, Optimal Contr. Appl. Methods, vol. 10, 2007, pp. 1–21.MathSciNetGoogle Scholar
  6. 331.
    Pettersson, S. and B. Lennartson, Controller Design of Hybrid Systems, in Lecture Notes in Computer Science, vol. 1201, Springer, Berlin, 1997, pp. 240–254.Google Scholar
  7. 260.
    Mahmoud, M. S. and Yuanqing Xia, Robust Filter Design for Piecewise Discrete-Time Systems with Time-Varying Delays, Int. J. Robust Nonlinear Contr., vol. 20, no. 3, 2010, pp. 540–560.Google Scholar
  8. 333.
    Pettersson, S. and B. Lennartson, Hybrid System Stability and Robustness Verification Using Linear Matrix Inequalities, Int. J. Contr., vol. 75, 2002, pp. 1335–1355.MathSciNetMATHCrossRefGoogle Scholar
  9. 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
  10. 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
  11. 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
  12. 28.
    Branicky, M., Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems, IEEE Trans. Automat. Contr., vol. 43, no. 4, 1998, pp. 475–582.MathSciNetMATHCrossRefGoogle Scholar
  13. 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
  14. 268.
    Mahmoud, M. S., Abdulla Ismail and F. M. AL-Sunni, A Parameterization Approach to Stability and Feedback Stabilization of Linear Time-Delay Systems, Proc. IME Part I- J. Syst. Contr. Eng., vol. 223, no. 17, 2009, pp. 929–939.Google Scholar
  15. 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
  16. 119.
    Hattingh, J. and M. Claassen, SecuringWater Quality for Life, Int. J. Water Resour. Dev., vol. 24, 2008, pp. 401–405.CrossRefGoogle Scholar
  17. 286.
    Mahmoud, M. S., Y. Shi and F. M. AL-Sunni, Dissipativity Analysis and Synthesis of a Class of Nonlinear Systems with Time-Varying Delays, J. Franklin Inst., vol. 346, 2009, pp. 570–592.MathSciNetMATHCrossRefGoogle Scholar
  18. 246.
    Mahmoud, M. S. and A. Y. AlRayyah, Adaptive Control of Systems with Mismatched Nonlinearities and Time-Varying Delays using State-Measurements, IET Contr. Theory Appl., vol. 4, no. 1, 2010, pp. 27–36.MathSciNetCrossRefGoogle Scholar
  19. 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
  20. 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
  21. 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
  22. 252.
    Mahmoud, M. S. and H. E. Emara-Shabaik, New \(\mathcal{H}_{2}\) Filter for Uncertain Singular Systems using Strict LMIs, J. Circuits, Syst. Signal Process., vol. 28, no. 5, 2009, pp. 665–677.MathSciNetMATHCrossRefGoogle Scholar
  23. 327.
    Persis, C. D., R. D. Santis and A. S. Morse, Supervisory Control with State-Dependent Dwell-Time Logic and Constraints, Automatica, vol. 40, 2004, pp. 269–275.MATHCrossRefGoogle Scholar
  24. 240.
    Mahmoud, M. S. and N. B. Almutairi, Improved Resilient Filtering for Linear Discrete-Time Systems, J. Math Contr. Sci. Appl., vol. 1, no. 2, 2007, pp. 351–364.Google Scholar
  25. 321.
    Palhares, R. M., P. Peres and C. de Souza, Robust \(\mathcal{H}_{\infty}\) Filtering for Linear Continuous-Time Uncertain Systems with Multiple Delays: An LMI Approach, Proceedings of the 3rd IFAC Conference Robust Control Design, Prague, Check Republic, 2000.Google Scholar
  26. 294.
    Milot, J., M. J. Rodriguez and J. B. Serodes Song, Contribution of Neural Networks for Modeling Trihalomethanes Occurrence in Drinking Water, J. Water Resour. Plann. Manage., vol. 128, 2002, pp. 370–376.CrossRefGoogle Scholar
  27. 281.
    Mahmoud, M. S., A. W. Saif and P. Shi, Stabilization of Linear Switched Delay Systems: \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Methods, J. Optim. Theory Appl., vol. 142, no. 3, July 2009, pp. 583–607.MathSciNetMATHCrossRefGoogle Scholar
  28. 316.
    Pagilla, P. R., Robust Decentralized Control of Large-Scale Interconnected Systems: General Interconnections, Proceedings of American Control Conference, San Diego, CA, 1999, pp. 4527–4531.Google Scholar
  29. 261.
    Mahmoud, M. S. and Yuanqing Xia, Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays, J. Optim. Theory Appl., vol. 143, no. 2, 2009, pp. 329–355.MathSciNetMATHCrossRefGoogle Scholar
  30. 325.
    Parlakci, M. N. A., Robust Stability of Uncertain Systems with Time-Varying State-Delayed Systems, IEE Proc.- Contr. Theory Appl., vol. 153, no. 4, 2006, pp. 469–477.MathSciNetCrossRefGoogle Scholar
  31. 26.
    Saif, A. W., M. S. Mahmoud and Y. Shi, A Parameterized Delay-Dependent Approach to Control of Uncertain Switched Discrete-Time Delay Systems, Int. J. Innovative Comput. Inf. Contr., vol. 5, no. 10, 2009, pp. 1071–1082.Google Scholar
  32. 74.
    Gahinet, P., A. Nemirovski, A. L. Laub and M. Chilali, LMI Control Toolbox, The Math Works, Boston, MA, 1995.Google Scholar
  33. 15.
    Benzaouia, A., E. De Santis, P. Caravani and N. Daraoui, Constrained Control of Switching Systems: A Positive Invariant Approach, Int. J. Contr., vol. 80, 2007, 1379–1387.MATHCrossRefGoogle Scholar
  34. 41.
    Cuzzola, F. A. and M. Morari, A Generalized Approach for Analysis and Control of Discrete-Time Piecewise Affine and Hybrid Systems, in Hybrid Systems: Computation and Control, Di Benedetto, M. D., San Giovanni-Vincentelli, A. L. (Editors), Springer, Berlin, 2001, pp. 135–164.Google Scholar
  35. 274.
    Mahmoud, M. S., E. K. Boukas and P. Shi, Resilient Feedback Stabilization of Discrete-Time Systems with Delays, IMA J. Math. Contr. Inf., vol. 25, no. 2, 2008, pp. 141–156.MathSciNetMATHCrossRefGoogle Scholar
  36. 301.
    Moon, Y. S., P. Park, W. H. Kwon and Y. S. Lee, Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems, Int. J. Contr., vol. 74, no. 14, 2001, pp. 1447–1455.MathSciNetMATHCrossRefGoogle Scholar
  37. 107.
    Haimes, Y. Y., Hierarchical Analyses of Water Resources Systems, McGraw-Hill, New York, NY, 1977.Google Scholar
  38. 307.
    Nesic, D. and D. Liberzon, A Unified Framework for Design and Analysis of Networked and Quantized Control Systems, IEEE Trans. Automat. Contr., vol. 54, 2009, pp. 732–747.MathSciNetCrossRefGoogle Scholar
  39. 234.
    Mahmoud, M. S., Stabilization of Time-Delay Systems by PID Controllers, Proceedings of the 6th International Multi-Conference on Systems, Signals and Devices (SSD’09), Djerba-Tunisia, March 23–26, 2009, Paper # 1569171107.Google Scholar
  40. 27.
    Boyd, S., L. El. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, {SIAM Stud. Appl. Math}., Philadelphia, 1994.CrossRefGoogle Scholar
  41. 332.
    Pettersson, S. and B. Lennartson, Stabilization of Hybrid Systems Using a Min-Projection Strategy, Proceedings of the 2001 American Control Conference, Arlington, VA, 2001, pp. 223–228.Google Scholar
  42. 228.
    Mahmoud, M. S., State-Feedback Stabilization of Linear Systems with Input and State Delays, Proc. IME Part I- J. Syst. Contr. Eng., vol. 233, no. 14, June 2009, pp. 557–565. DOI: 10.1243/09596518JSCE723.Google Scholar
  43. 312.
    Niculescu, S.-I., J.-M. Dion and L. Dugard, Robust Stabilization for Uncertain Time delay Systems Containing Saturating Actuators, IEEE Trans. Automat. Contr., vol. 41, 1996, pp. 742–747.MathSciNetMATHCrossRefGoogle Scholar
  44. 243.
    Mahmoud, M. S. and N. B. Almutairi, Stability and Implementable \(\mathcal{H}_{\infty}\) Filters for Singular Systems with Nonlinear Perturbations, Nonlinear Dyn., vol. 57, no. 6, 2009, pp. 401–410.MathSciNetMATHCrossRefGoogle Scholar
  45. 309.
    Nian, X. and R. Li, Robust Stability of Uncertain Large-Scale Systems with Time-Delay, Int. J. Syst. Sci., vol. 32, 2001, pp. 541–544.MathSciNetMATHGoogle Scholar
  46. 295.
    Miranda, M. F. and V. J. S. Leite, Convex Analysis and Synthesis for Uncertain Discrete-Time Systems with Time-Varying State-Delay, Proceedings of American Control Conference, Seattle, Washington, June 11–13, 2008, pp. 4910–4915.Google Scholar
  47. 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
  48. 284.
    Mahmoud, M. S., P. Shi and Y. Shi, Simultaneous \(\mathcal{H}_{2}/\mathcal{H}_{\infty}\) Control of Uncertain Jumping Systems with Functional Time-Delays, Int. J. Robust Nonlinear Contr., vol. 18, no. 3, 2008, pp. 296–318.MathSciNetCrossRefGoogle Scholar
  49. 271.
    Mahmoud, M. S., F. M. AL-Sunni and Y. Shi, Mixed \(\mathcal{H}_{2}-\mathcal{H}_{\infty}\) Control of Uncertain Jumping Time-Delay Systems, J. Franklin Inst., vol. 345, no. 5, 2008, pp. 536–552.MathSciNetMATHCrossRefGoogle Scholar
  50. 308.
    Nesic, D. and A. R. Teel, Input-to-State Stability of Networked Control Systems, Automatica, vol. 40, 2004, pp. 2121–2128.MathSciNetMATHGoogle Scholar
  51. 298.
    Montagner, V. F., V. J. S. Leite, S. Tarbouriech and P. L. D. Peres, Stability and Stabilizability of Discrete-Time Switched Linear Systems with State-Delay, Proceedings of American Control Conference, Portland, OR, 2005, pp. 3806–3811.Google Scholar
  52. 285.
    Mahmoud, M. S., Y. Shi and F. M. AL-Sunni, Robust \(\mathcal{H}_{2}\) Output Feedback Control for a Class of Time-Delay Systems, Int. J. Innovative Comput. Inf. Contr., vol. 4, no. 12, 2008, pp. 3247–3257.Google Scholar
  53. 314.
    Oucheriah, S., Decentralized Stabilization of Large-Scale Systems with Multiple Delays in the Interconnection, Int. J. Contr., vol. 73, 2000, pp. 1213–1223.MathSciNetMATHCrossRefGoogle Scholar
  54. 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
  55. 239.
    Mahmoud, M. S. and Abdulla Ismail, Resilient Control of Nonlinear Discrete-Time State-Delay Systems, Appl. Math Comput., vol. 206, no. 2, 2008, pp. 561–569.MathSciNetMATHCrossRefGoogle Scholar
  56. 248.
    Mahmoud, M. S. and Awatef Kamal M Ali, A Robust \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Control Approach to Uncertain Systems with Time-varying Delays, Proc. IME Part I- J Syst. Contr. Eng., vol. 223, no. 14, 2009, pp. 507–520.Google Scholar
  57. 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
  58. 34.
    Chen, W. H., Z. H. Guan and X. Lu, Delay-Dependent Guaranteed Cost Control for Uncertain Discrete-Time Systems with Delay, IEE Proc.-Contr. Theory Appl., vol. 150, 2003, pp. 412–416.CrossRefGoogle Scholar
  59. 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
  60. 324.
    Park, P. G. and J.W. Ko, Stability and Robust Stability for Systems with a Time-Varying Delay, Automatica, vol. 43, 2007, pp. 1855–1858.MathSciNetMATHCrossRefGoogle Scholar
  61. 289.
    Martinez, L. A. M. and C. H. Moog, New Insights on the Analysis of Nonlinear Time-Delay Systems: Application to The Triangular Equivalence, Syst. Contr. Lett., vol. 56, 2007, pp. 133–140.MATHCrossRefGoogle Scholar
  62. 216.
    Mahmoud, M. S., Robust Control and Filtering for Time-Delay Systems, Marcel-Dekker, New-York, NY, 2000.MATHGoogle Scholar
  63. 233.
    Mahmoud, M. S., Improved Stability and Stabilization Approach to Linear Interconnected Time-Delay Systems, Optimal Contr. Appl. Methods, vol. 31, no. 3, 2010, pp. 81–92.MATHCrossRefGoogle Scholar
  64. 320.
    Palhares, R. M., C. D. Campos, P. Y. Ekel, M. C. R. Leles and M. F. S. V. DAngelo, Delay-Dependent Robust \(\mathcal{H}_{\infty}\) Control of Uncertain Linear Systems with Lumped Delays, IEE Proc. Contr. Theory Appl., vol. 153, 2005, pp. 27–33.CrossRefGoogle Scholar
  65. 275.
    Mahmoud, M. S., E. K. Boukas and P. Shi, Robust Adaptive Control of Uncertain Discrete-Time State-Delay Systems, Comput. Math Appl., vol. 55, no. 11, 2008, pp. 2887–2902.MathSciNetMATHCrossRefGoogle Scholar
  66. 299.
    Montestruque, L. A. and P. J. Antsaklis, On the Model-based Control of Networked Systems, Automatica, vol. 39, 2003, pp. 1837–1843.MathSciNetMATHCrossRefGoogle Scholar
  67. 302.
    Morse, A. S., (Editor), Control using Logic-Based Switching, Springer, New York, NY, 1996.Google Scholar
  68. 292.
    Michel, A., Recent Trends in the Stability Analysis of Hybrid Dynamical Systems, IEEE Trans. Circuits Syst.-Part I, 46, 1999, pp. 120–134.MATHCrossRefGoogle Scholar
  69. 310.
    Niculescu, S.-I., On Delay-Dependent Stability Under Model Transformations of Some Neutral Linear Systems, Int. J. Contr., vol. 74, pp. 609–617.Google Scholar
  70. 311.
    Niculescu, S.-I., Delay Effects on Stability: A Robust Control Approach, Springer, Berlin, 2001.MATHGoogle Scholar
  71. 328.
    Petersen, I. R., A Stabilization Algorithm for a Class of Uncertain Linear Systems, Syst. Contr. Lett., vol. 8, 1987, pp. 351–357.MATHCrossRefGoogle Scholar
  72. 323.
    Park, J.-H., A New Delay-dependent Criterion for Neutral Systems with Multiple Delays, J. Comput. Appl. Math., vol. 136, 2001, pp. 177–184.MathSciNetMATHCrossRefGoogle Scholar
  73. 303.
    Mukaidani, H., An LMI Approach to Guaranteed Cost Control for Uncertain Time-Delay Systems, IEEE Trans. Circuits Syst.-I, vol. 50, 2003, pp. 795–800.MathSciNetCrossRefGoogle Scholar
  74. 247.
    Mahmoud, M. S. and A. Y. AlRayyah, Efficient Parameterization to Stability and Feedback Synthesis of Linear Time-Delay Systems, IET Contr. Theory Appl., vol. 3, no. 8, 2009, pp. 1107–1118.MathSciNetCrossRefGoogle Scholar
  75. 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
  76. 288.
    Mancilla-Aguilar, J. L. and R. A. Garcia, A Converse Lyapunov Theorem for Nonlinear Switched Systems, Syst. Contr. Lett., vol. 41, no. 1, 2000, pp. 67–71.MathSciNetMATHCrossRefGoogle Scholar
  77. 296.
    Molchanov A. P. and E. Pyatnitskiy, Criteria of Asymptotic Stability of Differential and Difference Inclusions Encountered in Control Theory, Syst. Contr. Lett., vol. 13, 1989, pp. 59–64.MathSciNetMATHCrossRefGoogle Scholar
  78. 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
  79. 304.
    Myshkis, A., Introduction to the Theory and Applications of Functional Differential Equations, Kluwer, The Netherlands, 1999.MATHGoogle Scholar
  80. 297.
    Montagner, V. F., V. J. S. Leite, R. C. L. F. Oliveira and P. L. D. Peres, State-Feedback Control of Switched Linear Systems: An LMI Approach, J. Comput. Appl. Math., vol. 194, 2006, pp. 192–206.MathSciNetMATHCrossRefGoogle Scholar
  81. 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
  82. 329.
    Petersen, I. R. and D. C. McFarlane, Optimal Guaranteed Cost Control and Filtering for Uncertain Linear Systems, IEEE Trans. Automat. Contr., vol. 39, 1994, pp. 1971–1977.MathSciNetMATHCrossRefGoogle Scholar
  83. 322.
    Park, P., A Delay-Dependent Stability Criterion for Systems with Uncertain Time-Invariant Systems, IEEE Trans. Automat. Contr., vol. 44, no. 4, 1999, pp. 876–879.MATHCrossRefGoogle Scholar
  84. 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
  85. 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
  86. 242.
    Mahmoud, M. S. and N. B. Almutairi, Decentralized Stabilization of Interconnected Systems with Time-Varying Delays, Eur. J. Contr., vol. 15, no. 6, 2009, pp. 624–633.MathSciNetMATHCrossRefGoogle Scholar
  87. 280.
    Mahmoud, M. S., A. W. Saif and P. Shi, Stabilization of Linear Switched Delay Systems: \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Methods, J. Optim. Theory Appl., vol. 142, no. 3, 2009, pp. 583–607.MathSciNetMATHCrossRefGoogle Scholar
  88. 363.
    Subbaroo Vemula, V. R., P. P. Mujumdar and S. Ghosh, Risk Evaluation in Water Quality Management of a River System, J. Water Resour. Plann. Manage., vol. 130, 2004, pp. 411–423.CrossRefGoogle Scholar
  89. 306.
    Narendra, K. S. and J. Balakrishnan, A common Lyapunov Function for Stable LTI Systems with Commuting A-Matrices, IEEE Trans. Automat. Contr., vol. 39, no. 12, 1994, pp. 2469–2471.MathSciNetMATHCrossRefGoogle Scholar
  90. 227.
    Mahmoud, M. S., Generalized \(\mathcal{H}_{2}\) Control of Switched Discrete-Time with Unknown Delays, Appl. Math Comput., vol. 311, no. 1, 2009, pp. 33–44.CrossRefGoogle Scholar
  91. 251.
    Mahmoud, M. S. and S. El-Ferik, New Stability and Stabilization Methods for Nonlinear Systems with Time-Varying Delays, Optimal Contr. Appl. Methods, vol. 31, no. 2, 2010, pp. 273–287.MathSciNetMATHGoogle Scholar
  92. 290.
    McClamroch, N. H. and I. Kolmanvsky, Performance Benefits of Hybrid Control Design for Linear and Nonlinear Systems, Proc. IEEE, vol. 88, 2000, pp. 1083–1096.CrossRefGoogle Scholar
  93. 232.
    Mahmoud, M. S., Delay-Dependent Dissipativity of Singular Time-Delay Systems, IMA J. Math. Contr. Inf., vol. 26, no. 1, 2009, pp. 45–58.MATHCrossRefGoogle Scholar
  94. 230.
    Mahmoud, M. S., Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays, J. Optim. Theory Appl., vol. 143, no. 5, 2009, pp. 497–518.MathSciNetMATHCrossRefGoogle Scholar
  95. 270.
    Mahmoud, M. S., F. M. AL-Sunni and Y. Shi, Dissipativity Results for Linear Singular Time-Delay Systems, Int. J. Innovative Comput. Inf. Contr., vol. 4, no. 11, 2008, pp. 2833–2845.Google Scholar
  96. 283.
    Mahmoud, M. S., P. Shi and Y. Shi, Simultaneous \(\mathcal{H}_{2}/\mathcal{H}_{\infty}\) Control of Uncertain Jumping Systems with Functional Time-Delays, Int. J. Robust Nonlinear Contr., vol. 18, no. 3, 2008, pp. 296–318.MathSciNetCrossRefGoogle Scholar
  97. 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
  98. 226.
    Mahmoud, M. S., Switched Discrete-Time with Time-Varying Delays: A Generalized \(\mathcal{H}_{2}\) Approach, Comput. Math Appl., vol. 57, no. 1, 2009, pp. 79–95.MathSciNetMATHCrossRefGoogle Scholar
  99. 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
  100. 300.
    Montestruque, L. A. and P. J. Antsaklis, Stability of Model-based Networked Control Systems with Time-Varying Transmission Times. IEEE Trans. Automat. Contr., vol. 49, no. 9, pp. 1562–1573.Google Scholar
  101. 319.
    Palhares, R. M., C. D. Campos, P. Y. Ekel, M. C. R. Leles and M. F. S. V. DAngelo, Delay-Dependent Robust \(\mathcal{H}_{\infty}\) Control of Uncertain Linear Systems with Time-Varying Delays, Comput. Math. Appl., vol. 50, 2005, pp. 13–32.MathSciNetMATHCrossRefGoogle Scholar
  102. 47.
    DeCarlo, R., M. Branicky, S. Pettersson and B. Lennartson, Perspectives and Results on the Stability and Stabilizability of Hybrid Systems, Proc. IEEE, vol. 88, 2000, pp. 1069–1082.CrossRefGoogle Scholar
  103. 241.
    Yuanqing Xia, Y., Zheng Zhu and M. S. Mahmoud, H2 control for Networked Control Systems with Markovian Data Losses and Delay, Proceedings of the 2nd International Symposium on Intelligent Informatics (ISII 2009), QinHuangDao, China, September 13–15, 2009, and in ICIC Express Letters (ICIC-EL).Google Scholar
  104. 229.
    Mahmoud, M. S., New Exponentially-Convergent State Estimation Method for Delayed Neural Networks, Neurocomputing, vol. 72, no. 16–18, 2009, pp. 3935–3942.CrossRefGoogle Scholar
  105. 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
  106. 231.
    Mahmoud, M. S., Stabilization of Linear Time-Delay Systems by Three-Term Controllers, Proceedings of the 3rd International Multi-Conference on Systems and Control (MSC 2009), Saint Petersburg, Russia, July 8–10, 2009, pp. 296–301.Google Scholar
  107. 259.
    Mahmoud, M. S. and Yuanqing Xia, Design of Reduced-Order \(\mathcal{L}_{2}-\mathcal{L}_{\infty}\) Filter for Singular for Discrete-Time Systems Using Strict LMIs, IET Contr. Theory Appl., vol. 4, no. 3, 2010, pp 509–519.CrossRefGoogle Scholar
  108. 272.
    Mahmoud, M. S., F. M. AL-Sunni and Y. Shi, Switched Discrete-Time Delay Systems: Delay-Dependent Analysis and Synthesis, J. Circuits, Syst. Signal Process., vol. 28, no. 5, 2009, pp. 735–761.MathSciNetMATHCrossRefGoogle Scholar
  109. 315.
    Overstreet, J. W. and A. Tzes, An Internet-Based Real-Time Control Engineering Laboratory, IEEE Contr. Syst. Mag., vol. 19, 1999, pp. 320–326.CrossRefGoogle Scholar
  110. 421.
    Yuanqing Xia, Y., Zheng Zhu and M. S. Mahmoud, H2 control for Networked Control Systems with Markovian Data Losses and Delay, Proceedings of the 2nd International Symposium on Intelligent Informatics (ISII 2009), QinHuangDao, China, September 13–15, 2009, and in ICIC Express Letters (ICIC-EL).Google Scholar

Copyright information

© 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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