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.