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Delay-dependent Robust Dissipative Control for Singular LPV Systems with Multiple Input Delays

  • Xin Wang
  • Xian ZhangEmail author
  • Xiaona Yang
Regular Papers Control Theory and Applications
  • 5 Downloads

Abstract

This paper addresses the robust dissipative control problem for the singular linear parameter-varying (LPV) systems with multiple input time-delays. First, by constructing the parameter-dependent Lyapunov functional, a delay-dependent robust dissipativity criterion for singular LPV systems with multiple state time-delays is proposed. Second, on the basis of linear matrix inequalities (LMIs) technique, a novel delay-dependent robust dissipativity-based controller for the singular LPV delay systems is designed. Furthermore, it is proved that the resultant closed-loop system via state feedback controller is admissible and strictly robustly (Q,S,R)-dissipative. Finally, the effectiveness of the proposed method is demonstrated by three numerical examples.

Keywords

Linear matrix inequalities multiple input time-delays robust dissipative control singular LPV systems 

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References

  1. [1]
    S. Lim and J. P. How, “Modeling and H¥ control for switched linear parameter–varying missile autopilot,” IEEE Transactions on control systems technology, vol. 11, no. 6, pp. 830–838, 2003.CrossRefGoogle Scholar
  2. [2]
    D. H. Lee, Y. H. Joo, and S. K. Kim, “FIR–type robust H2 and H¥ control of discrete linear time–invariant polytopic systems via memory state–feedback control laws,” International Journal of Control, Automation and Systems, vol. 13, no. 5, pp. 1047–1056, 2015.CrossRefGoogle Scholar
  3. [3]
    G. H. Yang and J. X. Dong, “Robust stability of polytopic systems via affine parameter–dependent Lyapunov functions,” SIAM Journal on Control and Optimization, vol. 47, no. 5, pp. 2642–2662, 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    B. Lu, F. Wu, and S.W. Kim, “Switching LPV control of an F–16 aircraft via controller state reset,” IEEE Transactions on Control Systems Technology, vol. 14, no. 2, pp. 267–277, 2006.CrossRefGoogle Scholar
  5. [5]
    X. J. Li and G. H. Yang, “Adaptive fault detection and isolation approach for actuator stuck faults in closed–loop systems,” International Journal of Control, Automation and Systems, vol. 10, no. 4, pp. 830–834, 2012.CrossRefGoogle Scholar
  6. [6]
    J. X. Dong and G. H. Yang, “Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties,” Automatica, vol. 49, no. 6, pp. 1821–1829, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Y. He, M. Wu, J. H. She, and G. P. Liu, “Parameterdependent Lyapunov functional for stability of time–delay systems with polytopic–type uncertainties,” IEEE Transactions on Automatic Control, vol. 49, no. 5, pp. 828–832, 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    X. Zhang, X. F. Fan, Y. Xue, and W. Cai, “Robust exponential passive filtering for uncertain neutral–type neural networks with time–varying mixed delays viaWirtinger–based integral inequality,” International Journal of Control, Automation and Systems, vol. 15, no. 2, pp. 585–594, 2017.CrossRefGoogle Scholar
  9. [9]
    H. M. Wang and G. H. Yang, “Robust H¥ filter design for affine fuzzy systems,” International Journal of Control, Automation, and Systems, vol. 11, no. 2, pp. 410–415, 2013.CrossRefGoogle Scholar
  10. [10]
    H. Wang, H. H. Ju, and Y. L. Wang, “H¥ switching filter design for LPV systems in finite frequency domain,” International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 503–510, 2013.CrossRefGoogle Scholar
  11. [11]
    X. Zhang, Y. Y. Han, L. G. Wu, and Y. T. Wang, “State estimation for delayed genetic regulatory networks with reaction–diffusion terms,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 2, pp. 299–309, 2018.MathSciNetCrossRefGoogle Scholar
  12. [12]
    X. Zhang, X. F. Fan, and L. G. Wu, “Reduced–and fullorder observers for delayed genetic regulatory networks,” IEEE Transactions on Cybernetics, vol. 48, no. 7, pp. 1989–2000, 2018.CrossRefGoogle Scholar
  13. [13]
    B. Niu and L. Li, “Adaptive backstepping–based neural tracking control for MIMO nonlinear switched systems subject to input delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 6, pp. 2638–2644, 2018.MathSciNetCrossRefGoogle Scholar
  14. [14]
    H. F. Li, N. Zhao, X. Wang, X. Zhang, and P. Shi, “Necessary and sufficient conditions of exponential stability for delayed linear discrete–time systems,” IEEE Transactions on Automatic Control, (in press), 2018. DOI: 10.1109/TAC.2018.2830638Google Scholar
  15. [15]
    F. B. Li and X. Zhang, “A delay–dependent bounded real lemma for singular LPV systems with time–variant delay,” International Journal of Robust and Nonlinear Control, vol. 22, no. 5, pp. 559–574, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Y. Zhang, F. Yang, and Q. L. Han, “H¥ control of LPV systems with randomly multi–step sensor delays,” International Journal of Control, Automation and Systems, vol. 12, no. 6, pp. 1207–1215, 2014.CrossRefGoogle Scholar
  17. [17]
    J. C. Willems, “Dissipative dynamical systems, part I: general theory,” Archive for rational mechanics and analysis, vol. 45, no. 5, pp. 321–351, 1972.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    X. Lou and B. Cui, “Passive control of uncertain multiple input–delayed systems using reduction method,” Mathematics and Computers in Simulation, vol. 20, pp. 2258–2271, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M. Meisami–Azad, J. Mohammadpour, and K. M. Grigoriadis, “Dissipative analysis and control of state–space symmetric systems,” Automatica, vol. 45, no. 6, pp. 1574–1579, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Z. G. Wu, P. Shi, H. Y. Su, and R. Q. Lu, “Dissipativitybased sampled–data fuzzy control design and its application to truck–trailer system,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 5, pp. 1669–1679, 2015.CrossRefGoogle Scholar
  21. [21]
    Z. G. Wu, S. L. Dong, H. Y. Su, and C. D. Li, “Asynchronous dissipative control for fuzzy Markov jump systems,” IEEE Transactions on Cybernetics, vol. 48, no. 8, pp. 2426–2436, 2018.CrossRefGoogle Scholar
  22. [22]
    J. Tao, Z. G. Wu, H. Y. Su, Y. Q. Wu, and D. Zhang, “Asynchronous and resilient filtering for Markovian jump neural networks subject to extended dissipativity,” IEEE Transactions on Cybernetics, (in press), 2017. DOI:10.1109/TCYB.2018.2824853Google Scholar
  23. [23]
    B. Niu, D. Wang, H. Li, X. J. Xie, N. D. Alotaibi, and F. E. Alsaadi, “A novel neural–network–based adaptive control scheme for output–constrained stochastic switched nonlinear systems,” IEEE Transactions on Neural Networks and Learning Systems, (in press), 2017. DOI:10.1109/TSMC.2017.2777472Google Scholar
  24. [24]
    X. M. Liu, S. T. Li, and K. J. Zhang, “Optimal control of switching time in switched stochastic systems with multiswitching times and different costs,” International Journal of Control, vol. 90, no. 8, pp. 1604–1611, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    F. B. Li, P. Shi, C. C. Lim, and L. G. Wu, “Fault detection filtering for nonhomogeneous markovian jump systems via fuzzy approach,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 1, pp. 131–141, 2018.CrossRefGoogle Scholar
  26. [26]
    T. B. Wu, F. B. Li, C. H. Yang, and W. H. Gui, “Eventbased fault detection filtering for complex networked jump systems,” IEEE/ASME Transactions on Mechatronic, vol. 23, no. 2, pp. 497–505, 2018.CrossRefGoogle Scholar
  27. [27]
    M. S. Mahmoud, Y. Shi, and F. M. AL–Sunni, “Dissipativity analysis and synthesis of a class of nonlinear systems with time–varying delays,” Journal of the Franklin Institute, vol. 346, no. 6, pp. 570–592, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    J. Zhou, Y. Zhang, Q. L. Zhang, and M. Bo, “Dissipative analysis for nonlinear singular systems with time–delay,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2461–2470, 2017.CrossRefGoogle Scholar
  29. [29]
    Z. G. Wu, J. H. Park, H. Y. Su, and J. Chu, “Dissipativity analysis for singular systems with time–varying delays,” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4605–4613, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    Z. G. Feng, J. Lam, and H. J. Gao, “a–dissipativity analysis of singular time–delay systems,” Automatica, vol. 47, no. 11, pp. 2548–2552, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    M. S. Mahmoud, “Delay–dependent dissipativity of singular time–delay systems,” IMA Journal of Mathematical Control and Information, vol. 26, no. 1, pp. 45–58, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    Z. G. Feng and J. Lam, “Dissipative control and filtering of discrete–time singular systems,” International Journal of Systems Science, vol. 47. no. 11, 2532.2542, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    I. Masubuchi, “Output feedback controller synthesis for descriptor systems satisfying closed–loop dissipativity,” Automatica, vol. 43, no. 2, pp. 339–345, 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    Z. G. Wu, J. H. Park, H. Y. Su, and J. Chu, “Admissibility and dissipativity analysis for discrete–time singular systems with mixed time–varying delays,” Applied Mathematics and Computation, vol. 218, no. 13, pp. 7128–7138, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    B. Y. Zhu, Q. L. Zhang, and C. L. Chang, “Delaydependent dissipative control for a class of non–linear system via takagi–sugeno fuzzy descriptor model with time delay,” IET Control Theory & Applications, vol. 8, no. 7, pp. 451–461, 2014.MathSciNetCrossRefGoogle Scholar
  36. [36]
    C. S. Han, L. G. Wu, P. Shi, and Q. S. Zeng, “Passivity and passification of T–S fuzzy descriptor systems with stochastic perturbation and time delay,” IET Control Theory & Applications, vol. 7, no. 13, pp. 1711–1724, 2013.MathSciNetCrossRefGoogle Scholar
  37. [37]
    Z. Su, J. Ai, Q. L. Zhang, and N. X. Xiong, “An improved robust finite–time dissipative control for uncertain fuzzy descriptor systems with disturbance,” International Journal of Systems Science, vol. 48, no. 8, pp. 1581–1596, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    Z. G. Wu, J. H. Park, H. Y. Su, and J. Chu, “Delaydependent passivity for singular Markov jump systems with time–delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 3, pp. 669–681, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    F. B. Li, C. L. Du, C. H. Yang, and W. H. Gui, “Passivitybased asynchronous sliding mode control for delayed singular Markovian jump systems,” IEEE Transactions on Automatic Control, vol. 63, no. 8, pp. 2715–2721, 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    Z. G. Wu, J. H. Park, H. Y. Su, and J. Chu, “Reliable passive control for singular systems with time–varying delays,” Journal of Process Control, vol. 23, no. 8, pp. 1217–1228, 2013.CrossRefGoogle Scholar
  41. [41]
    J. X. Lin, Y. Shi, S. M. Fei, and Z. W. Gao, “Reliable dissipative control of discrete–time switched singular systems with mixed time delays and stochastic actuator failures,” IET Control Theory & Applications, vol. 7, no. 11, pp. 1447–1462, 2013.MathSciNetCrossRefGoogle Scholar
  42. [42]
    L. Dai, Singular Control Systems, Springer–Verlag, Berlin, 1989.CrossRefzbMATHGoogle Scholar
  43. [43]
    K. Gu, “An integral inequality in the stability problem of time–delay systems,” Proc. the 39th IEEE Conf. Decision Control, pp. 2805–2810, 2000.Google Scholar
  44. [44]
    D. Yue, J. Lam, and D. W. C. Ho, “Reliable H¥ control of uncertain descriptor systems with multiple time delays,” IEE Proceedings–Control Theory and Applications, vol. 150, pp. 557–564, 2003.CrossRefGoogle Scholar
  45. [45]
    P. Gahinet, P. Apkarian, and M. Chilali, “Affine parameterdependent Lyapunov functions and real parametric uncertainty,” IEEE Transactions on Automatic control, vol. 41, no. 3, pp. 436–442, 1996.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical Science, and the Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex SystemsHeilongjiang UniversityHarbinChina

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