D-stability of polytopes of polynomial matrices: characterization through LMIs

Improved linear matrix inequality conditions are given to test if the zeros of all polynomial matrices belonging to a polytope lie inside a specific convex region D in the complex plane. These conditions, formulated at the vertices of the polytopic uncertainty domain, generalize and encompass recently appeared results. Examples and numerical experiments from both continuous-time (left half-plane) and discrete-time (unit disk) systems are presented in order to compare this formulation with previous results from the literature.