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H∞ control problem of linear periodic piecewise time-delay systems

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  • Xiaochen Xie
  • James Lam
  • Panshuo Li

Abstract

This paper investigates the H∞ control problem based on exponential stability and weighted L2-gain analyses for a class of continuous-time linear periodic piecewise systems with time delay. A periodic piecewise Lyapunov–Krasovskii functional is developed by integrating a discontinuous time-varying matrix function with two global terms. By applying the improved constraints to the stability and L2-gain analyses, sufficient delay-dependent exponential stability and weighted L2-gain criteria are proposed for the periodic piecewise time-delay system. Based on these analyses, an H∞ control scheme is designed under the considerations of periodic state feedback control input and iterative optimisation. Finally, numerical examples are presented to illustrate the effectiveness of our proposed conditions.

Suggested Citation

  • Xiaochen Xie & James Lam & Panshuo Li, 2018. "H∞ control problem of linear periodic piecewise time-delay systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(5), pages 997-1011, April.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:5:p:997-1011
    DOI: 10.1080/00207721.2018.1440028
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