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Dissipative analysis for nonlinear singular systems with time-delay

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  • Control Theory and Applications
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Abstract

This paper is concerned with the dissipative control problem for a class of nonlinear singular systems with time-delay. The quadratic supply rate with coefficient matrix Q > 0 and Q ≤ 0 are both discussed. Based on the Lyapunov stability theory, sufficient conditions are given to guarantee that the system is strictly dissipative via linear matrix inequality technique. Then congruent transformation method and Schur complement lemma are respectively used to determine corresponding proportional and derivative feedback controller for Q > 0 and Q ≤ 0. At last, two examples involve a practical example are given to verify the effectiveness of the method proposed in this paper.

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References

  1. J. C. Willems, “Dissipative dynamical systems-part 1: general Theory,” Archives of Rational Mechanics Analysis, vol. 45, no. 5, pp. 321–351, 1972. [click]

    Article  MATH  Google Scholar 

  2. J. C. Willems, “Dissipative dynamical systems-part 2: linear systems with quadratic supply rates,” Archives of Rational Mechanics Analysis, vol. 45, no. 5, pp. 352–393, 1972. [click]

    Article  MATH  Google Scholar 

  3. M. Malek-Zavarei and M. Jamshidi, “Time-delay systems: analysis, optimization and applications,” Sole Distributors for the U.S.A. and Canada, Elsevier Science Pub. Co, 1987.

    Google Scholar 

  4. D. Zhai, Q. L. Zhang, and J. H. Li, “Fault detection for singular multiple time-delay systems with application to electrical circuit,” Journal of the Franklin Institute, vol. 351, no. 12, pp. 5411–5436, 2014. [click]

    Article  MathSciNet  Google Scholar 

  5. S. I. Niculescu, Delay Effects on Stability, Springer-Verlag, Berlin, 2001.

    MATH  Google Scholar 

  6. E. Fridman, “Stability of linear descriptor systems with time delay: a Lyapunov-based approach,” Journal of Mathematical Analysis and Applications, vol. 273, no. 1, pp. 24–44, 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. E. Fridman and U. Shaked, “A descriptor system approach to H ∞ control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 253–270, 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  8. E. K. Boukas and Z. K. Liu, “Delay-dependent stability analysis of singular linear continuous-time system,” IEE Proceedings - Control Theory and Applications, vol. 150, no. 4, pp. 394–398, 2003.

    Article  Google Scholar 

  9. C. Lin, Q. G. Wang, and H. L. Tong, “Stability and stabilization of a class of fuzzy time-delay descriptor systems,” IEEE Transactions on Fuzzy Systems, vol. 14, no. 4, pp. 542–551, 2006. [click]

    Article  Google Scholar 

  10. H. L. Gao, X. U. Bu-Gong, and Y. G. Zhang, “Delaydependent robust stability criteria for two classes of uncertain singular time-delay systems,” IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 880–885, 2007. [click]

    Article  MathSciNet  Google Scholar 

  11. D. Zhai, L. w. An, J. H. Li, and Q. L. Zhang, “Delaydependent adaptive dynamic surface control for nonlinear strict-feedback delayed systems with unknown dead zone,” Journal of the Franklin Institute, vol. 353, no. 2, pp. 297–302, 2015.

    Google Scholar 

  12. Y. F. Feng, “Delay-dependent stability criteria for singular time-delay systems,” Zidonghua Xuebao/acta Automatica Sinica, vol. 36, no. 3, pp. 433–437, 2010.

    MathSciNet  Google Scholar 

  13. Y. M. Li, S. S. Tong, and T. S. Li, “Hybrid fuzzy adaptive output feedback control design for uncertain MIMO nonlinear systems with time-varying delays and input saturation,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 4, pp. 841–853, 2016. [click]

    Article  Google Scholar 

  14. H. Su, X. Ji, and J. Chu, “Delay-dependent robust control for uncertain singular time-delay systems,” Asian Journal of Control, vol. 1, no. 5, pp. 1234–1241, 2007. [click]

    MathSciNet  Google Scholar 

  15. C. M. Qi, X. Z. Dong, and L. Liu, “Dissipativit analysis and synthesis of singular systems via delta operator method,” Proceedings of the 2015 Chinese Intelligent Automation Conference. Springer Berlin Heidelberg, pp. 17–24, 2015.

    Google Scholar 

  16. S. Santra, H. R. Karimi, R. Sakthivel, and S. M. Anthoni, “Dissipative based adaptive reliable sampled-data control of time-varying delay systems,” International Journal of Control Automation and Systems, vol. 14, no. 1, pp. 39–50, 2016. [click]

    Article  Google Scholar 

  17. Saravanakumar and Syed, “Robust H ∞ control for uncertain Markovian jump systems with mixed delays,” Chinese Physics B, vol. 25, no. 7, 2016.

    Google Scholar 

  18. Y. M. Li and S. C. Tong, “Adaptive fuzzy output-feedback control of pure-feedback uncertain nonlinear systems with unknown dead-zone,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 5, pp. 1341–1347, 2014. [click]

    Article  Google Scholar 

  19. D Zhai, L. W. An, D. Ye, and Q. L. Zhang, “Adaptive reliable H ∞ static output feedback control against Markovian jumping sensor failures,” IEEE Transactions on Neural Networks and Learning Systems, DOI: 10.1109/TNNLS.2016.2639290.

  20. Y. M. Li, S. C. Tong, and T. S. Li, “Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems,” IEEE Transactions on Cybernetics, vol. 45, no. 1, pp. 138–149, 2015. [click]

    Article  Google Scholar 

  21. S. L. Campbell, Singular Systems of Differential Equations, Pitman, London, 1980.

    MATH  Google Scholar 

  22. L. Dai, Singular Control Systems, Springer, Berlin, 1989.

    Book  MATH  Google Scholar 

  23. L. Yu, Robust Control -LMI Method, Tsinghua University Press, 2002.

    Google Scholar 

  24. S. Y. Xu, P.V. Dooren, R. Stefan, and J. Lam, “Robust stability and stabilization for singular systems with state delay and parameter uncertainty,” IEEE Transactions on Automatic Control, vol. 47, no. 7, pp. 1122–1128, 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  25. H. Zhang, H. C. Yan, and Q. J. Chen, “Stability and dissipative analysis for a class of stochastic system with timedelay,” Journal of the Franklin Institute, vol. 347, no. 5, pp. 829–893, 2010.

    Google Scholar 

  26. M. Meisami-Azad, J. Mohammadpour, and K. M. Grigoriadis, “Dissipative analysis and control of state-space symmetric systems,” Automatica, vol. 45, pp. 1574–1579, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  27. J. C. Ren and Q. L. Zhang, “Robust H∞ control for uncertain descriptor systems by proportional-derivative state feedback,” International Journal of Control, vol. 83, no. 1, pp. 89–96, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  28. H.W. Braden, “The equations AX±XA=B,” Siam Journal on Matrix Analysis & Applications, vol. 20, pp. 295–302, 1998.

    Article  MATH  Google Scholar 

  29. D. Zhai, L. W. An, J. H. Li, and Q. L. Zhang, “Fault detection for stochastic parameter-varying Markovian jump systems with application to networked control systems,” Applied Mathematical Modelling, vol. 40, no. 3, pp. 2368–2383, 2016. [click]

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Systems Science, Northeastern University, Shenyang, Liaoning, 110819, China

    Juan Zhou, Yue Zhang & Qingling Zhang

  2. School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, Liaoning, 110034, China

    Men Bo

Authors
  1. Juan Zhou
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  2. Yue Zhang
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  3. Qingling Zhang
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  4. Men Bo
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Corresponding author

Correspondence to Qingling Zhang.

Additional information

Recommended by Associate Editor Juhoon Back under the direction of Editor PooGyeon Park. This work was supported by the Fundamental Research Funds for the Central Universities (N160503004), the Natural Science Foundation of China (61673099).

Zhou Juan received the M.S. degree from Jilin University in 2006. She is currently a lecture in Northeastern University. Her research interests are in the areas of descriptor systems.

Zhang Yue received the Ph.D. degree in Control theory and control engineering, Northeastern University, China, in March 2007, the M.S. degree, in Basic mathematics, Northeastern University, China, in March 2004 and the B.S. degree in Mathematics, Liaoning Normal University, China, in July 1999.

Zhang Qingling received the B.S. and M.S. degrees from the Mathematics Department and the Ph.D. degree from the Automatic Control Department of Northeastern University, Shenyang, China, in 1982, 1986 and 1995, respectively. Dr. Zhang is now a Professor at Northeastern University. His research interests include descriptor system.

Men Bo received the Ph.D. degree from the Institute of System Sciences, Northeastern University in 2013. She is currently a lecture in Shenyang Normal University. Her research interests are in the areas of switched systems, singular systems.

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Zhou, J., Zhang, Y., Zhang, Q. et al. Dissipative analysis for nonlinear singular systems with time-delay. Int. J. Control Autom. Syst. 15, 2461–2470 (2017). https://doi.org/10.1007/s12555-016-0259-4

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  • DOI: https://doi.org/10.1007/s12555-016-0259-4

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