Abstract
The common Lyapunov function problem is a problem which examines existence conditions of a common Lyapunov function for several linear time-invariants systems. The problem arises, for example, when we consider the stability of a switching system which consists of several linear time-invariant systems. Although the problem for the existence of a quadratic Lyapunov function has been discussed, l∞ Lyapunov function counterpart seems to have not been treated. In this study, we examine the common l∞ Lyapunov function problem for both continuous-time and discrete-time systems. For both cases conditions for some subsets of the set of systems which have a common l∞ Lyapunov function were clarified.
