Stability of linear descriptor systems with delay: A Lyapunov-based approach

The Lyapunov second method is developed for linear coupled systems of delay differential and functional equations. By conventional approaches such equations may be reduced to the neutral systems and the known results for the latter may be exploited. In the present paper we introduce a new approach by constructing a Lyapunov-Krasovskii functional that corresponds directly to the descriptor form of the system. Moreover, by representing a neutral system in the descriptor form we obtain new stability criteria for neutral systems which are less conservative than the existing results. Sufficient conditions for delay-dependent/delay-independent stability and for robustness of stability with respect to small delays are given in terms of linear matrix inequalities. Illustrative examples show the effectiveness of the method.