A Less Conservative LMI Condition for Robust ${cal D}$ -Stability of Polynomial Matrix Polytopes—A Projection Approach

This technical note investigates the problem of checking robust D-stability of a polytope of polynomial matrices. Finsler´s projection lemma is taken to derive a new sufficient condition in terms of a linear matrix inequality (LMI) feasibility problem. The basic idea behind this condition is to lift the existing stability condition into the one of larger space by means of Finsler´s lemma and, based on it, to introduce additional decision variables. Examples are given to show that the proposed condition can yield less conservative results than the previous one.