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arXiv · 2209.04869

Systems with both constant and time-varying delays: a switched systems approach and application to observer-controller co-design

Thiago Alves Lima·Matteo Della Rossa·Frédéric Gouaisbaut·Raphaël Jungers·Sophie Tarbouriech
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Abstract

In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of path-complete Lyapunov techniques along with the proposition of a new modified functional to obtain convex analysis conditions while avoiding the need of computing a dwell time for each mode in a switched system representation, as usual in the \textit{switched approach} for time-delay systems. Furthermore, we leverage the developed analysis to obtain LMIs for the closed-loop stabilization of systems with time-varying sensor delays by means of an observer-based compensator. A numerical example illustrates the proposed methods.

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Thiago Alves Lima, Matteo Della Rossa, Frédéric Gouaisbaut, Raphaël Jungers, Sophie Tarbouriech. 2022-09-11. Systems with both constant and time-varying delays: a switched systems approach and application to observer-controller co-design. https://arxiv.org/abs/2209.04869

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