Stability Analysis and State-Feedback Stabilization of LPV Time-Delay Systems with Piecewise Constant Parameters subject to Spontaneous Poissonian Jumps

TL;DR

This paper presents a stability analysis and state-feedback stabilization method for LPV systems with stochastic piecewise constant delays modeled by Poissonian jumps, using tractable LMIs for controller synthesis.

Contribution

It introduces a novel approach to analyze and stabilize LPV time-delay systems with stochastic parameters via integral-free LMIs, enhancing computational feasibility.

Findings

Derived sufficient conditions for stability using stochastic Lyapunov functionals.

Provided tractable LMI-based synthesis conditions for gain-scheduled controllers.

Validated the approach through illustrative examples.

Abstract

This paper discusses the stability analysis of linear parameter varying systems with a parameter-dependent delay where the parameters are assumed to be stochastic piecewise constants under spontaneous Poissonian jumps. Based on stochastic Lyapunov-Krasovskii functionals, we also provide sufficient synthesis conditions for the gain-scheduled state-feedback controller with memory in terms of parameter-dependent linear matrix inequalities (LMIs). Such synthesis conditions are computationally intractable due to the presence of integral terms. However, we show that these LMIs can be equivalently represented by integral-free LMIs, which are computationally tractable. Finally, we illustrate the applicability of the results through examples.