Abstract
A common quadratic Lyapunov function guarantees asymptotic stability of a set of systems. The common Lyapunov function problem to be study here, is to specify a set of systems which have a common quadratic Lyapunov function guaranteeing asymptotic stability of its every member system. Several sufficient condition of linear systems which have a common quadratic Lyapunov function, are already known. Furthermore, there exist some parallel results between for continuous-time and discrete-time linear systems. In this paper, we add a new sufficient condition of discrete-time systems with this property using diagonally dominant matrices. This condition provides a counterpart of a known result for continuouse-time systems.
