On common quadratic Lyapunov functions for stable discrete-time LTI systems

Abstract

This paper deals with the question of the existence of weak and strong common quadratic Lyapunov functions (CQLFs) for stable discrete-time linear time-invariant (LTI) systems. The main result of the paper provides a simple characterization of pairs of such systems for which a weak CQLF of a given form exists but for which no strong CQLF exists. An application of this result to second-order discrete-time LTI systems is presented.