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Output Feedback Passification of Switched Continuous-Time Linear Systems Subject to Saturating Actuators

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Abstract

This paper is concerned with the output feedback passification of switched continuous-time linear systems with actuation saturation. A switching law and saturated output feedback controllers with the form of quasi-linear parameter-varying are designed such that the closed-loop switched system with actuator saturation is passive, and the system state remains inside an invariant ellipsoid, which meet the requirements of passivity and saturation simultaneously. Since the system state is often unavailable, we consider the issue of how to design dynamic output feedback controllers using only partial state measurements. Moreover, the switching law is designed to depend only on the state of the dynamic output feedback controllers, which renders the switched system passivity even the subsystems are non-feedback passive. Sufficient conditions for the existence of the switching and output feedback control law are derived in terms of linear matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed method.

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References

  1. A. Cepeda, A. Astolfi, Control of a planar system with quantized and saturated input/output. IEEE Trans. Circuits Syst. I Reg. Papers 55(3), 932–942 (2008)

    Article  MathSciNet  Google Scholar 

  2. 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 

  3. N.H. ElFara, P. Mhaskar, P.D. Christofides, Output feedback control of switched nonlinear systems using multiple lyapunov functions. Syst. Control Lett. 54(12), 1163–1182 (2005)

    Article  Google Scholar 

  4. H.J. Fang, Z.L. Lin, T.S. Hu, Analysis of linear systems in the presence of actuator saturation and \(L_{2}\)-disturbances. Automatica 40(7), 1229–1238 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Gahinet, P. Apkarian, A linear matrix inequality approach to \(H_{\infty }\) control. Int. J. Robust Nonlinear Control 4(4), 421–448 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. J.C. Geromel, P. Colaneri, P. Bolzern, Passivity of switched linear systems: analysis and control design. Syst. Control Lett. 61(4), 549–554 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  7. T.S. Hu, Z.L. Lin, A complete stability analysis of planar linear systems under saturation. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(4), 498–512 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. T.S. Hu, Z.L. Lin, Control Systems with Actuator Saturation: Analysis and Design (Birkhuser, Boston, 2001)

    Book  Google Scholar 

  9. M. Johansson, A. Rantzer, Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Trans. Autom. Control 43(4), 555–559 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Li, J. Zhao, Passivity and feedback passification of switched discrete-time linear systems. Syst. Control Lett. 63(11), 1073–1081 (2012)

    Google Scholar 

  11. J. Li, J. Zhao, \(H_{\infty }\) output tracking control for discrete-time switched systems based on switching method. Circuits Syst. Signal Process 32(5), 2487–2502 (2013)

    Article  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. H. Lin, P.J. Antsaklis, Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans. Autom. Control 54(2), 308–322 (2009)

    Article  MathSciNet  Google Scholar 

  14. L. Lu, Z.L. 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 

  15. M.S. Mahmoud, Y. Xia, Robust stability and stabilization of a class of nonlinear switched discrete-time systems with time-varying delays. J. Optim. Theory Appl. 143(2), 329–355 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. J. Rubio, W. Yu, Stability analysis of nonlinear system identification via delayed neural networks. IEEE Trans. Circuits Syst. II Expr. Briefs 54(2), 161–165 (2007)

    Article  Google Scholar 

  17. P. Shi, Y.Y. Yin, F. Liu, Gain-scheduled worst case control on nonlinear stochastic systems subject to actuator saturation and unknown information. J. Optim. Theory Appl. 156(3), 844–858 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  18. X.M. Sun, G.P. Liu, D. Rees, W. Wang, Delay-dependent stability for discrete systems with large delay sequence based on switching techniques. Automatica 44(11), 2902–2908 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. X.M. Sun, G.P. Liu, W. Wang, D. Rees, Stability analysis for networked control systems based on average dwell time method. Int. J. Robust Nonlinear Control 20(15), 1774–1784 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  20. J.C. Willems, Dissipative dynamical systems. Eur. J. Control 13(2–3), 134–151 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  21. F. Wu, Z.L. 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 

  22. B. Xiao, Q.L. Hu, P. Shi, Attitude stabilization of spacecrafts under actuator saturation and partial loss of control effectiveness. IEEE Trans. Control Syst. Technol. 21(6), 2251–2263 (2013)

    Article  Google Scholar 

  23. Y.Y. Xu, Y.M. Li, S.C. Tong, Fuzzy adaptive actuator failure compensation dynamic surface control of multi-input and multi-output nonlinear systems. Int. J. Innov. Comput. Inform. Control 9(12), 4875–4888 (2013)

    Google Scholar 

  24. H. Yang, V. Cocquempot, B. Jiang, Fault tolerance analysis for switched systems via global passivity. IEEE Trans. Circuits Syst. II 55(12), 1279–1283 (2008)

    Article  Google Scholar 

  25. L.X. Zhang, P. Shi, Stability, \(L_{2}\)-gain and asynchronous \(H_{\infty }\) control ofdiscrete-time switched systems with average dwell time. IEEE Trans. Autom. Control 54(9), 2193–2200 (2009)

    Google Scholar 

  26. X.Q. Zhang, J. Zhao, G.M. Dimirovski, \(L_{2}\)-Gain analysis and control synthesis of uncertain discrete-time switched linear systems with time delay and actuator saturation. Int. J. Control 84(10), 1746–1758 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  27. G.J. Zhang, C.S. Han, Y. Guan, L.G. Wu, Exponential stability analysis and stabilization of discrete-time nonlinear switched systems with time delays. Int. J. Innov. Comput. Inform. Control 8(3(A)), 1973–1986 (2012)

    Google Scholar 

  28. J. Zhao, D.J. Hill, A notion of passivity for switched systems with state-dependent switching. J. Control Theory Appl. 4(1), 70–75 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. J. Zhao, D.J. Hill, Dissipativity theory for switched systems. IEEE Trans. Autom. Control 53(4), 941–953 (2008)

    Article  MathSciNet  Google Scholar 

  30. J. Zhao, D.J. Hill, Passivity and stability of switched systems: a multiple storage function method. Syst. Control Lett. 57(2), 158–164 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  31. X.D. Zhao, L.X. Zhang, P. Shi, M. Liu, Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans. Autom. Control 57(7), 1809–1815 (2012)

    Article  MathSciNet  Google Scholar 

  32. X.D. Zhao, L.X. Zhang, P. Shi, M. Liu, Stability of switched positive linear systems with average dwell time switching. Automatica 48(6), 1132–1137 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  33. X.D. Zhao, L.X. Zhang, P. Shi, Stability of a class of switched positive linear time-delay systems. Int. J. Robust Nonlinear Control 23(5), 578–589 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  34. 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  MATH  MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants 61304058 and 61233002, and IAPI Fundamental Research Funds under Grant 2013ZCX03-01, Fundamental Research Funds for the Central Universities under Grant N130604003.

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Authors and Affiliations

  1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, People’s Republic of China

    Xiao-Qi Zhao & Jun Zhao

  2. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, People’s Republic of China

    Xiao-Qi Zhao & Jun Zhao

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  1. Xiao-Qi Zhao
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  2. Jun Zhao
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Correspondence to Jun Zhao.

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Zhao, XQ., Zhao, J. Output Feedback Passification of Switched Continuous-Time Linear Systems Subject to Saturating Actuators. Circuits Syst Signal Process 34, 1343–1361 (2015). https://doi.org/10.1007/s00034-014-9903-5

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  • DOI: https://doi.org/10.1007/s00034-014-9903-5

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