Stability Analysis of a Class of Discontinuous Discrete-Time Systems

TL;DR

This paper develops a method for analyzing the stability of certain discontinuous discrete-time systems using Lyapunov functions and linear matrix inequalities, providing a systematic approach for ensuring global exponential stability.

Contribution

It introduces a novel stability analysis framework for discontinuous systems modeled as feedback interconnections with set-valued nonlinearities, using optimization and LMI techniques.

Findings

Sufficient LMI conditions for stability are derived.

Numerical examples validate the theoretical stability criteria.

Abstract

The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent representation, based on a constrained optimization problem, is proposed to represent the set-valued nonlinearity via a collection of linear and quadratic constraints. Relying on this description and on the use of a generalized quadratic set-valued Lyapunov functions, sufficient conditions in the form of linear matrix inequalities for global exponential stability are obtained. Numerical examples corroborate the theoretical findings.