This paper studies the problem of the relations between existence conditions of common quadratic Lyapunov functions and common 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, desired relations are determined. It turns out that although the relation is equivalent for a single stable system, the existence condition of common quadratic type is implied by that of common infinity-norm type for a set of systems. Several existence conditions of a common infinity-norm Lyapunov are also presented.
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