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Control Synthesis of Discrete-Time Switched Linear Systems with Input Saturation Based on Minimum Dwell Time Approach

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Abstract

This paper investigates the control synthesis problem for discrete-time switched linear systems with input saturation. Based on minimal dwell time approach, state feedback controller and dynamic output feedback controller are respectively designed in terms of LMIs. The corresponding optimization problems are formulated to obtain a bigger attractive region. Compared with previous results, our proposed results can recover part of attractive region. Finally, numerical example is presented to illustrate the effectiveness and value of our obtained results.

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References

  1. A. Benzaouia, L. Saydy, O. Akhrif, Stability and control synthesis of switched systems subject to actuator saturation, in Proc. American Control Conf. (2004), pp. 5818–5823

    Google Scholar 

  2. A. Benzaouia, O. Akhrif, L. Saydy, Stabilization of switched systems subject to actuator saturation by output feedback, in Proc. 45th IEEE Conf. Decision and Control (2006), pp. 777–782

    Chapter  Google Scholar 

  3. A. Benzaouia, O. Akhrif, L. Saydy, Stabilisation and control synthesis of switching systems subject to actuator saturation. Int. J. Syst. Sci. 41(4), 397–409 (2010)

    Article  MathSciNet  Google Scholar 

  4. J. Daafouz, P. Riedinger, C. Iung, Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Autom. Control 47(11), 1883–1887 (2002)

    Article  MathSciNet  Google Scholar 

  5. H. Fang, Z. Lin, T. Hu, Analysis of linear systems in the presence of actuator saturation and L 2-disturbances. Automatica 40(7), 1229–1238 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. J.P. Hespanha, A.S. Morse, Stability of switched systems with average dwell time, in Proc. 38th IEEE Conf. Decision and Control (1999), pp. 2655–2660

    Google Scholar 

  7. T. Hu, Z. Lin, Control Systems with Actuator Saturation: Analysis and Design (Birkhäuser, Boston, 2001)

    Book  MATH  Google Scholar 

  8. T. Hu, Z. Lin, B.M. Chen, An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica 38(2), 351–359 (2002)

    Article  MATH  Google Scholar 

  9. T. Hu, Z. Lin, B.M. Chen, Analysis and design for discrete-time linear systems subject to actuator saturation. Syst. Control Lett. 45(2), 97–112 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. W. Gao, R.R. Selmic, Neural network control of a class of nonlinear systems with actuator saturation. IEEE Trans. Neural Netw. 17(1), 147–156 (2006)

    Article  MATH  Google Scholar 

  11. H. Gao, X. Yang, P. Shi, Multi-objective robust H control of spacecraft rendezvous. IEEE Trans. Control Syst. Technol. 17(4), 794–802 (2009)

    Article  MathSciNet  Google Scholar 

  12. D. Liberzon, A.S. Morse, Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19(5), 59–70 (1999)

    Article  Google Scholar 

  13. D. Liberzon, Switching in Systems and Control (Birkhäuser, Boston, 2003)

    Book  MATH  Google Scholar 

  14. F. Long, W. Wei, On neural network switched stabilization of SISO switched nonlinear systems with actuator saturation, in ISNN 2007, Part I. LNCS, vol. 4491 (2007), pp. 296–305

    Google Scholar 

  15. L. Lu, Z. Lin, Design of switched linear systems in the presence of actuator saturation. IEEE Trans. Autom. Control 53(6), 1536–1542 (2008)

    Article  MathSciNet  Google Scholar 

  16. L. Lu, Z. Lin, H. Fang, L 2-gain analysis for a class of switched systems. Automatica 45(4), 965–972 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. M.S. Mahmoud, F.M. Al-Sunni, Y. Shi, Switched discrete-time delay systems: delay-dependent analysis and synthesis. Circuits Syst. Signal Process. 28(5), 735–761 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. W. Ni, D. Cheng, Control of switched linear systems with input saturation. Int. J. Syst. Sci. 41(9), 1057–1065 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Pettersson, B. Lennartson, Stabilization of hybrid systems using a min-projection strategy, in Proc. American Control Conf. (2001), pp. 223–228

    Google Scholar 

  20. S. Pettersson, Synthesis of switched linear systems, in Proc. 42th IEEE Conf. Decision and Control (2003), pp. 5283–5288

    Google Scholar 

  21. Y. Song, Z. Xiang, Q. Chen, W. Hu, Control of switched systems with actuator saturation. J. Control Theory Appl. 4(1), 38–43 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. W. Sun, H. Gao, O. Kaynak, Finite frequency H control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 19(2), 416–422 (2011)

    Article  Google Scholar 

  23. X. Sun, J. Zhao, D.J. Hill, Stability and L 2-gain analysis for switched delay systems: a delay-dependent method. Automatica 42(10), 1769–1774 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. Z. Sun, S.S. Ge, Switched Linear Systems: Control and Design (Springer, London, 2005)

    MATH  Google Scholar 

  25. F. Wu, Z. Lin, Q. Zheng, Output feedback stabilization of linear systems with actuator saturation. IEEE Trans. Autom. Control 52(1), 122–128 (2007)

    Article  MathSciNet  Google Scholar 

  26. G. Zhai, B. Hu, K. Yasuda, A.N. Michel, Disturbance attenuation properties of time-controlled switched systems. J. Franklin Inst. 338(7), 765–779 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  27. L. Zhang, H. Gao, Asynchronously switched control of switched linear systems with average dwell time. Automatica 46(5), 953–958 (2010)

    Article  MATH  Google Scholar 

  28. L. Zhang, E.-K. Boukas, P. Shi, Exponential H filtering for uncertain discrete-time switched linear systems with average dwell time: a μ-dependent approach. Int. J. Robust Nonlinear Control 18(11), 1188–1207 (2008)

    Article  MathSciNet  Google Scholar 

  29. X. Zhang, J. Zhao, G.M. Dimirovski, L 2-gain analysis and control synthesis of uncertain switched linear systems subject to actuator saturation. Int. J. Syst. Sci. (2010). doi:10.1080/00207721.2010.521597

    Google Scholar 

  30. W.-A. Zhang, L. Yu, Stability analysis for discrete-time switched time-delay systems. Automatica 45(10), 2265–2271 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. Q. Zheng, F. Wu, Output feedback control of saturated discrete-time linear systems using parameter-dependent Lyapunov functions. Syst. Control Lett. 57(11), 896–903 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  32. G. Zong, L. Hou, Y. Wu, Robust l 2l guaranteed cost filtering for uncertain discrete-time switched system with mode-dependent time-varying delays. Circuits Syst. Signal Process. 30(1), 17–33 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  33. Z. Zuo, Y. Wang, An improved set invariance analysis and gain-scheduled control of LPV systems subject to actuator saturation. Circuits Syst. Signal Process. 26(5), 635–649 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  34. Z. Zuo, Y. Wang, On enlarging the domain of attraction for linear systems subject to actuator saturation. Int. J. Gen. Syst. 37(2), 239–248 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  35. Z. Zuo, D.W.C. Ho, Y. Wang, Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation. Automatica 46(3), 569–576 (2010)

    Article  MATH  Google Scholar 

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Correspondence to Shumin Fei.

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Chen, Y., Fei, S., Zhang, K. et al. Control Synthesis of Discrete-Time Switched Linear Systems with Input Saturation Based on Minimum Dwell Time Approach. Circuits Syst Signal Process 31, 779–795 (2012). https://doi.org/10.1007/s00034-011-9347-0

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  • DOI: https://doi.org/10.1007/s00034-011-9347-0

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