The Computation of Common Infinity-norm Lyapunov Functions for Linear Switched Systems

Abstract

This paper studies the problem of the computation of common infinity-norm Lyapunov functions. For a set of continuous-time LTI systems or discrete-time LTI systems whose system matrices are upper triangular form or lower triangular form, it is proved that there exist common infinity-norm Lyapunov functions for them. Then four algorithms of computing common infinity-norm Lyapunov functions are presented. Finally, several examples are listed.