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Non-fragile H∞ control of periodic piecewise time-varying systems based on matrix polynomial approach

Author

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  • Yun Liu
  • Panshuo Li
  • Bin Zhang

Abstract

This paper investigates the problem of non-fragile $ H_{\infty } $ H∞ control for periodic piecewise time-varying systems. Based on a Lyapunov function with continuous time-varying Lyapunov matrix polynomial, and combining with the positiveness and negativeness properties of matrix polynomials, the $ H_{\infty } $ H∞ performance analysis is first accomplished. Then consider two types of controller gain perturbations that are formulated by time-varying matrix parameters and norm-bounded uncertainties. The additive and multiplicative non-fragile controllers to guarantee the $ H_{\infty } $ H∞ performance of the system are formed, of which the controller gain could be solved with linear matrix inequalities directly. The designed non-fragile $ H_{\infty } $ H∞ controller is desirable in applications. Finally, numerical examples demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Yun Liu & Panshuo Li & Bin Zhang, 2021. "Non-fragile H∞ control of periodic piecewise time-varying systems based on matrix polynomial approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(4), pages 805-820, March.
    • Handle: RePEc:taf:tsysxx:v:52:y:2021:i:4:p:805-820
    DOI: 10.1080/00207721.2020.1841846
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