Hybrid State Feedback, Robust H ∞  Control for a Class Switched Systems with Nonlinear Uncertainty

Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 129)

Abstract

The problem of robust H  ∞  control for a class of uncertain nonlinear switched systems is addressed through hybrid state feedback control strategy, based on multiple Lyapunov function techniquefor all admissible uncertainties. The state feedback control for each each subsystem and switching Laws to guarantee both asymptotically stability of the resulting closed-loop systems and prescribed L 2 gain from disturbance input to controller output are designed. The necessary and sufficient conditions of robust H  ∞  control for the problem to be solvable is also derived in terms of partial differential inequalities are given. An illustrate example is given to show the effectiveness of the method.

Keywords

Lyapunov Function State Feedback State Feedback Control Controller Output Disturbance Input 
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References

  1. 1.
    Apkarian, P., Gahinet, P.: A convex characterization of gain-scheduled controller. IEEE Trans. on Automatic Control 40(5), 854–864 (1959)MathSciNetGoogle Scholar
  2. 2.
    Cheng, D., Guo, L., Huang, J.: On quadratic Lyapunov functions. IEEE Trans. on Automatic Control 48(5), 885–890 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ji, Z., Wang, L.: Disturbance attenuation of uncertain switched linear systems. In: Proc. of the 43rd IEEE Conf. on Decision and Control, pp. 3708–3718. IEEE Press, Atlantis (2004)Google Scholar
  4. 4.
    Kim, S., Campbell, S.A., Liu, X.: Stability of A Class of linear switching Systems with Time Delay. IEEE Trans. on Circuits and Systems-I: Regular Papers 53(2), 384–393 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Lu, G.P., Zheng, Y.F., Ho, D.W.C.: Nonlinear robust H  ∞  control via dynamic output feedback. Systems Control Letters 39(2), 193–202 (2000)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Shen, T., Tamura, K.: Robust H  ∞  control of uncertain nonlinear system via state feedback. IEEE Trans. on Automatic Control 40(4), 766–768 (1995)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Xie, G., Wang, L.: New results on stability of switched linear systems. In: Proc. of the 42nd IEEE Conf. on Decision and Control, pp. 6265–6270. IEEE press, Hawaii (2003)Google Scholar
  8. 8.
    Zhao, S., Zhao, J.: H  ∞  control for cascade minimum-phase switched nonlinear Systems. Journal of Control Theory and Applications 2(2), 163–173 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Automatic EngineeringZhonshan College, Uest of ChinaZhongshanP.R. China
  2. 2.Department of Mathematical SciencesBinghamton University-SunyBinghamtonU.S.A.

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