Stability of Switched Linear Systems under Dwell Time Switching with Piece-Wise Quadratic Functions

TL;DR

This paper develops a method using piece-wise quadratic Lyapunov functions and bilinear matrix inequalities to determine stability and minimum dwell time in switched linear systems, with convergence properties as the number of functions increases.

Contribution

It introduces a novel approach employing piece-wise quadratic functions and bilinear matrix inequalities to analyze stability and dwell time in switched systems.

Findings

Sequence of upper bounds converges to minimum dwell time with more quadratic functions.

Numerical examples demonstrate the effectiveness of the proposed method.

Method provides sufficient conditions for stability under dwell-time switching.

Abstract

This paper provides sufficient conditions for stability of switched linear systems under dwell-time switching. Piece-wise quadratic functions are utilized to characterize the Lyapunov functions and bilinear matrix inequalities conditions are derived for stability of switched systems. By increasing the number of quadratic functions, a sequence of upper bounds of the minimum dwell time is obtained. Numerical examples suggest that if the number of quadratic functions is sufficiently large, the sequence may converge to the minimum dwell-time.