Abstract
This paper studies the problem of the relations between existence conditions of common quadratic and those of com-mon infinity-norm Lyapunov functions for sets of continuous-time linear time-invariant systems. Based on the equivalence between the robust stability of a class of time-varying systems and the existence of a common infinity-norm Lyapunov function for the corresponding set of linear time-invariant systems, the relations are determined. It turns out that although the relation is an equivalent one for a single stable system, the existence condition of common infinity-norm type is implied by that of common quadratic type for a set of systems. Several existence conditions of a common infinity-norm Lyapunov are also presented for the purpose of easy checking.
