H-infinite Stability Analysis and Controller Synthesis for Markov Jump System with Pure Time-Delays

Some H-infinite stability control methods for Markov jump systems with pure time-delays are discussed in this paper, and some theorems are obtained to stabilize the systems with some anti-disturbance performances. Firstly, the system description with some distributed time delays is obtained by using a system transformation. Secondly, according to a positive energy functional and LMI technique, some sufficient conditions are achieved for making sure the system is stable. If those criteria are solvable, some controllers can be gotten to stabilize system and the energy gain from the external disturbance to the system output is constrained to be no larger than a prescribed value. Furthermore, some examples are given to show that the obtained methods are useful.