Stability analysis and stabilization of stochastic linear impulsive, switched and sampled-data systems under dwell-time constraints

TL;DR

This paper extends stability analysis and control methods from deterministic to stochastic impulsive, switched, and sampled-data systems under dwell-time constraints, using convex LMIs and sum of squares techniques.

Contribution

It introduces convex clock-dependent LMI conditions for stochastic systems, enabling robust analysis and state-feedback stabilization under dwell-time constraints.

Findings

Conditions are formulated as convex LMIs for stability analysis.

The approach is applicable to robust control design.

Numerical examples demonstrate effectiveness and accuracy.

Abstract

Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting. The concepts of mean-square stability and dwell-times are utilized in order to formulate relevant stability conditions for such systems. These conditions are formulated as convex clock-dependent linear matrix inequality conditions that are applicable to robust analysis and control design, and are verifiable using discretization or sum of squares techniques. Stability conditions under various dwell-time conditions are obtained and non-conservatively turned into state-feedback stabilization conditions. The results are finally applied to the analysis and control of stochastic sampled-data systems. Several comparative examples demonstrate the accuracy and the tractability of the approach.