Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching

This paper deals with admissibility analysis for discrete-time singular Markov jump systems (SMJSs) with asynchronous switching, which means the switching of controllers is asynchronous with the switching of subsystems. The switching delay and state delay are modeled as Markov chains. The resulting closed-loop system is modeled as a singular system with a Markovian jumping vector and two Markovian jumping parameters. A new necessary and sufficient condition for regularity, causality and stability of the closed-loop system is proposed. Based on this, a state feedback controller is designed in terms of a strict linear matrix inequality (LMI) to guarantee the admissibility of SMJSs with asynchronous switching. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.