A necessary and sufficient condition for robust stability analysis of continuous-time descriptor polytopic systems

This paper investigates robust stability of continuous-time descriptor polytopic systems (CTDPSs). A necessary and sufficient condition for robust stability is first given as parameterized linear matrix inequalities (LMIs) whose variable matrices are homogeneous polynomial matrices of the multi-parameters. Furthermore, it is shown that the parameterized LMIs is reduced to parameter-independent and finite-dimensional LMIs. Finally, two numerical examples are given, illustrating the effectiveness of the proposed method.