Relations between Common Lyapunov Functions of Quadratic and Infinity-Norm Forms for a Set of Discrete-Time LTI Systems

Abstract

This paper studies the problem of the relations between existence conditions of common quadratic and those of common infinity-norm Lyapunov functions for sets of discrete-time linear time-invariant (LTI) systems. It turns out that although the relation is an equivalent one for single stable systems, the existence condition of common infinity-norm type is strictly implied by that of common quadratic type for the set of systems.