State feedback control of Markovian jump systems with Markovian delay and uncertain transition probability

This paper is addressed with the networked-based state feedback control issue for a class of discrete-time Markovian jump linear systems (MJLS) with the random sensor to controller (S-C) time delay and the uncertain transition probability. Considering the random time delay occurring in feedback communication link, the resulting closed-loop system is modeled as a discrete-time Markovian jump linear delay system governed by two mutual independence Markov chains. A new stability criterion is established within the Markovian jump framework by applying a Lyapunov stability theory and linear matrix inequalities (LMI) technique. A simulation example illustrates the validity and feasibility of the method.