Stability analysis and state-feedback control of LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps

TL;DR

This paper analyzes the stability and control of LPV systems with piecewise constant parameters experiencing Poissonian jumps, using infinite-dimensional LMIs and sum of squares programming, and proposes an integral-free LMI condition for controller design.

Contribution

It introduces a novel stability and performance analysis framework for LPV systems with stochastic jumps, including an integral-free LMI condition for control synthesis.

Findings

Provided stability conditions via infinite-dimensional LMIs.

Developed an integral-free LMI for controller design.

Validated approach through multiple examples.

Abstract

LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps are a class of systems that does not seem to have been thoroughly considered in the literature. We partially fill this gap here by providing sufficient stability and performance analysis conditions stated in terms of infinite-dimensional LMI problems that can be solved using sum of squares programming. A particularity of the obtained conditions lies in the presence of an integral term leading to some technical difficulties when attempting to obtain convex conditions for the design of a gain-scheduled state-feedback controller. This difficulty is circumvented by relying on a recent result for time-delay systems analysis and an equivalent integral-free LMI condition is obtained. The approach is illustrated through several examples.