D-stability analysis of polynomial matrices and polynomial matrix polytopes by using LMI approach

New LMI conditions are present to analyze the stability of polynomial matrices and polynomial matrix polytopes in an intersecting region D. During the analysis, the intersecting region D is described by disjoint regions and the problem to analyze the stability of polynomial matrices and polytopes in intersection D is transformed to analyze the stability in each disjoint D-region respectively. With this strategy, the stability of polynomial matrices and polytopes in an arbitrary D-region is checked successfully. To solve LMI problem in Matlab, the real-valued LMI conditions of all complex-valued LMI conditions are developed as well. Finally, numerical examples are provided to illustrate the effects of these new conditions.