A parameter-dependent Lyapunov function for a polytope of matrices
T. Mori, H. Kokame · IEEE Transactions on Automatic Control · 2000
A new sufficient condition for a polytope of matrices to be Hurwitz-stable is presented. The stability is a consequence of the existence of a parameter-dependent quadratic Lyapunov function, which is assured by a certain linear constraint for generating extreme matrices of the polytope. The condition can be regarded as a duality of the known extreme point result on quadratic stability of matrix polytopes, where a fixed quadratic Lyapunov function plays the role. The obtained results are applied to a polytope of second-degree polynomials for illustration.