Analyzing robust D-stability and D-stabilization for discrete descriptor systems subjected to norm-bounded uncertainties in the coefficient matrix

This paper investigates the problems of robust D-stability and D-stabilization for linear discrete uncertain descriptor systems ties in the whole system matrices cover that in the coefficient matrix E. We assume that the coefficient matrix E is rank-invariant, that is, rank(E) = r ≤ n for all admissible uncertainties. Thus, we consider the robustness analysis problem as two cases: the right-descriptor case and the left-descriptor case. Two necessary and sufficient D-stability conditions are developed for the first and second cases. Then, based on the above mentioned conditions, by applying a new augmentation method, the sufficient D-stabilization conditions will be presented for both cases. Both the D-stability and the D-stabilization conditions are obtained based on linear matrix inequalities. Finally, illustrative instances are given to testify the application of the proposed method for the two cases.