A polytopic quadratic Lyapunov functions approach to stability of a matrix polytope

It is known that a polytope of matrices is stable if there exists a positive-definite quadratic function that is a Lyapunov function common to all the vertex members. This simple criterion is extended to the case where a multituple of positive-definite quadratic functions is available. Some classes of such multituples that ensure the stability of the polytope are defined. Their inclusion relation is clarified. It is shown that one of the classes provides an easy-to-compute criterion for the stability of a matrix polytope. A systematic use of the criterion is demonstrated by an example concerning the stability of a linear system with unknown parameters