Admissibility and static output-feedback stabilization of singular Markovian jump systems with defective statistics of modes transitions

Abstract

This paper presents a necessary and sufficient condition for discrete-time singular Markovian jump linear systems with defective statistics of modes transitions to be regular, causal, and stochastically stable. The static output-feedback stabilization problem for discrete-time singular Markovian jump linear system with defective statistics of modes transitions is studied. Furthermore, the defective statistics about modes transitions are studied by considering the uncertain transition probabilities and partially unknown transition probabilities situations account in a composite way. The closed-loop system is represented in an augmented form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a sufficient condition for the existence of desired controllers is established. An extension to mode-independent static output-feed stabilization is provided as well.