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Dissipativity-based Framework for Stability Analysis of Aperiodically Sampled Nonlinear Systems with Time-varying Delay

Abstract : In this paper, we provide novel conditions for stability analysis of aperiodically sampled nonlinear control systems subjected to time-varying delay. The proposed approach can also deal with cases in which delay is larger than the sampling interval. It is applicable to a general class of nonlinear systems and provides sufficient criteria for stability that aid in making trade-offs between control performance and the bounds on sampling interval and delay. As a stepping stone, a preliminary and generic result based on dissipativity, is introduced to analyse the exponential stability of a class of feedback-interconnected systems. The nonlinear sampled-data system is remodelled to consider the effects of sampling and delay in the dissipativity framework, as perturbations to the nominal closed-loop system. This leads to constructive stability conditions for a continuous time closed-loop system given by the feedback interconnection of the nominal closed-loop system and an operator(s) that captures the effects of sampling and delay. For Linear Time-Invariant (LTI) systems, we recover simple Linear Matrix Inequality (LMI) and frequency domain conditions previously proposed in the robust control framework.
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https://hal.inria.fr/hal-03156571
Contributor : Jijju Thomas <>
Submitted on : Tuesday, March 2, 2021 - 3:22:26 PM
Last modification on : Tuesday, March 30, 2021 - 2:10:06 PM

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Jijju Thomas, Christophe Fiter, Laurentiu Hetel, Nathan van de Wouw, Jean-Pierre Richard. Dissipativity-based Framework for Stability Analysis of Aperiodically Sampled Nonlinear Systems with Time-varying Delay. Automatica, Elsevier, In press. ⟨hal-03156571⟩

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