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Stabilisation for 2-D discrete-time switched nonlinear systems with mixed time-varying delays under all modes unstable

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  • Dan Peng
  • Hanmei Nie

Abstract

The problem of delay-dependent stability is concerned for two-dimensional switched systems in Fornasini-Marchesini local state-space model with mixed time-varying delays and with a class of generalised Lipschitz nonlinearities in this paper. The mixed time-varying delays consist of both the discrete and the distributed delays, and the time-varying delays are allowed in the states. Adopting the fast average dwell-time switching technique with Lyapunov functional, a sufficient condition of the exponential stability for two-dimensional nonlinear switched systems with all subsystems unstable is derived in terms of linear matrix inequality. Specifically, two-dimensional Abel lemma-based finite-sum inequalities approach and Jensen inequalities approach are applied to reduce the conservativeness of the result. The obtained result on stability analysis is then utilised to design a dynamic output feedback controller to stabilise the nonlinear closed-loop switched system. Finally, two numerical examples are shown to demonstrate the validity of the proposed results.

Suggested Citation

  • Dan Peng & Hanmei Nie, 2022. "Stabilisation for 2-D discrete-time switched nonlinear systems with mixed time-varying delays under all modes unstable," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(4), pages 757-777, March.
    • Handle: RePEc:taf:tsysxx:v:53:y:2022:i:4:p:757-777
    DOI: 10.1080/00207721.2021.1972356
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