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.

Dissipativity-based conditions for the feedback stabilization of systems with time-varying input delays

“…An extension to the case of inputsaturated nonlinear systems in differential-algebraic representation (DAR) was also recently studied (Alves Lima et al, 2022). Dissipativity theory has also been recently studied for the stability analysis of aperiodically sampled nonlinear systems with time-varying delay (Thomas et al, 2021).…”