Abstract:

The problems of robust stability and robust stabilization via dynamic output feedback for uncertain discrete-time Markov jump descriptor systems with time-varying delays are discussed, where the uncertain is the norm-bounded parameter uncertainty and the delays are time-varying. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the discussed system is transformed into a discrete-time Markov jump standard linear system. Then the transformed system is discussed.By constructing a novel Lyapunov-Krasovskii functional, a sufficient condition for the system to be regular, causal and robust stochastically stable is established in terms of linear matrix inequalities (LMIs). And the dynamic output feedback controllers with full and partial knowledge of transition probabilities are obtained, respectively. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Key words: discrete-time Markov jump descriptor system; time-varying delay; output feedback stabilization; linear matrix inequality (LMI)