Stabilization of continuous-time Markov jump linear systems with defective statistics of modes transitions

Abstract

This paper concerns the stabilization problem of a class of Markov jump linear system (MJLS) with defective statistics of modes transitions in the continuous-time domain. Differing from the recent separate studies on the so-called uncertain transition probabilities (TPs) and partially unknown TPs, the defective statistics about modes transitions in this study take the two situations into account in a composite way. The scenario is more practicable in that it divides the TPs into three sets: known, uncertain and unknown. The necessary and suffcient conditions for the stability and stabilization of the underlying system are obtained by fully using the properties of the transition rate matrix (TRM) and the convexity of uncertain domains. The monotonicity, in concern of the existence of the admissible stabilizing controller, is observed when the unknown elements become uncertain and the intervals of the uncertain ones become tighter. Numerical examples are provided to verify the theoretical findings.