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Stabilization of a class of switched systems with state constraints

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Abstract

This paper investigates the stabilization problem for a class of switched systems with state constraints in both continuous-time and discrete-time contexts. The state constraints are converted into state saturations by limiting the state in a unit hypercube. An improved average dwell time method is presented to take into account different decay rates of a Lyapunov function related to an active subsystem according to the saturations occurring or not. Sufficient conditions for stability and stabilizability of the switched system with state constraints are derived; meanwhile, the stabilizing state feedback controllers are designed. An application to a longitudinal motion of highly maneuverable aircraft technology (HiMAT) vehicle is given to illustrate the applicability and the effectiveness of the proposed method.

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References

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

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Zhao, J., Dimirovski, G.M.: Quadratic stability of switched nonlinear systems. IEEE Trans. Autom. Control 49(4), 574–578 (2004)

    Article  MathSciNet  Google Scholar 

  4. Yang, H., Dimirovski, G.M., Zhao, J.: Switched fuzzy systems: modeling and control. Stud. Comput. Intell. 109, 169–184 (2008)

    Article  Google Scholar 

  5. Li, J., Yang, G.H.: Fault detection and isolation for discrete-time switched linear systems based on average dwell-time method. Int. J. Syst. Sci. (2012). doi:10.1080/00207721.2012.704091

    Google Scholar 

  6. Zhao, J., Hill, D.J.: Vector L 2-gain and stability of feedback switched systems. Automatica 45(7), 1703–1707 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lian, J., Zhang, K.: Exponential stability for switched Cohen-Grossberg neural networks with average dwell time. Nonlinear Dyn. 63(3), 331–343 (2011)

    Article  MathSciNet  Google Scholar 

  8. Zhao, X.G., Li, J., Ye, D.: Fault detection for switched systems with finite frequency specifications. Nonlinear Dyn. (2012). doi:10.1007/s11071-012-0464-5

    Google Scholar 

  9. Barkhordari, Y.M., Jahed-Motlagh, M.R.: Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization. Chem. Eng. J. 155(3), 838–843 (2009)

    Article  Google Scholar 

  10. Lin, H., Antsaklis, P.J.: Stability and persistent disturbance attenuation properties for a class of networked control systems: switched system approach. Int. J. Control 78(18), 1447–1458 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lee, T.C., Jiang, Z.P.: Uniform asymptotic stability of nonlinear switched systems with an application to mobile robots. IEEE Trans. Autom. Control 53(5), 1235–1252 (2008)

    Article  MathSciNet  Google Scholar 

  12. Bao, W., Li, B., Chang, J.T., Niu, W.Y., Yu, D.R.: Switching control of thrust regulation and inlet buzz protection for ducted rocket. Acta Astronaut. 67(8), 764–773 (2010)

    Article  Google Scholar 

  13. Bao, W., Qi, Y.W., Chang, J.T.: Multi-objective regulating and protecting control for ducted rocket using a bumpless transfer scheme. J. Aerosp. Eng. (2012). doi:10.1177/0954410011433237

    Google Scholar 

  14. Long, L.J., Zhao, J.: Global stabilization for a class of switched nonlinear feedforward systems. Syst. Control Lett. 60(9), 734–738 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Long, L.J., Zhao, J.: Global stabilisation of switched nonlinear systems in p-normal form with mixed odd and even powers. Int. J. Control 84(10), 1612–1626 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, J., Yang, G.H.: Asynchronous fault detection filter design approach for discrete-time switched linear systems. Int. J. Robust Nonlinear Control (2012). doi:10.1002/rnc.2875

    Google Scholar 

  17. Ma, R.C., Zhao, J.: Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings. Automatica 46(11), 1819–1823 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(4), 475–482 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhao, J., Hill, D.J.: L 2-gain and H ∞ control for switched systems. Automatica 44, 1220–1232 (2008)

    Article  MathSciNet  Google Scholar 

  20. Wang, D., Wang, W., Shi, P.: H ∞ filtering of discrete-time switched systems with state delays via switched Lyapunov function approach. IEEE Trans. Autom. Control 52(8), 1520–1525 (2007)

    Article  Google Scholar 

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

    Google Scholar 

  22. Lian, J., Wang, M.: Sliding-mode control of switched delay systems with nonlinear perturbations: average dwell time approach. Nonlinear Dyn. 62(4), 791–798 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Sun, X.M., Zhao, J., Hill, D.: 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. Zhai, G.S., Hu, B., Yasuda, K., Michel, A.N.: Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach. Int. J. Syst. Sci. 32(8), 1055–1061 (2001)

    MathSciNet  MATH  Google Scholar 

  25. Wang, D., Wang, W., Shi, P.: Exponential H ∞ filtering for switched linear systems with interval time-varying delay. Int. J. Robust Nonlinear Control 19(5), 532–551 (2009)

    Article  MATH  Google Scholar 

  26. Zhao, X.D., Zhang, L.X., Shi, P., Liu, M.: Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEE Trans. Autom. Control. (2011). doi:10.1109/TAC.2011.2178629

    Google Scholar 

  27. Richter, H.: A multi-regulator sliding mode control strategy for output-constrained systems. Automatica 47(10), 2251–2259 (2011)

    MathSciNet  MATH  Google Scholar 

  28. Glattfelder, A.H., Schaufelberger, W.: Control Systems with Input and Output Constraints. Advanced Textbooks in Control and Signal Processing. Springer, London (2003)

    Book  MATH  Google Scholar 

  29. Zhao, Y.Y., Xu, J.: Using the delayed feedback control and saturation control to suppress the vibration of the dynamical system. Nonlinear Dyn. 67(1), 735–753 (2012)

    Article  MATH  Google Scholar 

  30. Hu, Q.L.: Robust adaptive sliding mode attitude maneuvering and vibration damping of three-axis-stabilized flexible spacecraft with actuator saturation limits. Nonlinear Dyn. 55(4), 301–321 (2009)

    Article  MATH  Google Scholar 

  31. Xu, X.P., Antsaklis, P.J.: On time optimal control of integrator switched systems with state constraints. Nonlinear Anal. 62(8), 1453–1465 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  32. Yfoulis, C.A.: Constrained switching stabilization of linear uncertain switched systems using piecewise linear Lyapunov functions. Trans. Inst. Meas. Control 32(5), 529–566 (2010)

    Article  Google Scholar 

  33. Hou, L., Michel, A.N.: Asymptotic stability of systems with saturation constraints. Trans. Autom. Control 43(8), 1148–1154 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  34. Liu, D., Michel, A.N.: Dynamical Systems with Saturation Nonlinearities: Analysis and Design. Springer, London (1994)

    Book  MATH  Google Scholar 

  35. Fang, H.J., Lin, Z.L.: Stability analysis for linear systems under state constraints. IEEE Trans. Autom. Control 49(6), 950–955 (2004)

    Article  MathSciNet  Google Scholar 

  36. Zhang, L.X., Shi, P.: Stability, L 2-gain and asynchronous H ∞ control of discrete-time switched systems with average dwell time. IEEE Trans. Autom. Control 54(9), 2193–2200 (2009)

    MathSciNet  Google Scholar 

  37. Hou, Y.Z., Dong, C.Y., Wang, Q.: Adaptive control scheme for linear uncertain switched systems. In: AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu, Hawaii, pp. 1–12. American Institute of Aeronautics and Astronautics Inc., Honolulu (2008)

    Google Scholar 

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Acknowledgements

This work was supported by the Chinese National Fundamental Research Program under 2009CB320601, NSFC under Grants 61174073 and 90816028. The authors also gratefully acknowledge the helpful comments and suggestions from the reviewers and the associate editor.

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Authors and Affiliations

  1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, P.R. China

    Qingyu Su & Jun Zhao

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  1. Qingyu Su
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  2. Jun Zhao
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Correspondence to Qingyu Su.

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Su, Q., Zhao, J. Stabilization of a class of switched systems with state constraints. Nonlinear Dyn 70, 1499–1510 (2012). https://doi.org/10.1007/s11071-012-0550-8

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  • DOI: https://doi.org/10.1007/s11071-012-0550-8

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