Stability Analysis of Discrete-Time Semi-Markov Jump Linear Systems With Time Delay

The stability and stabilization problems for discrete-time semi-Markov jump linear systems with time delay are discussed. By virtue of a novel Lyapunov–Krasovskill functional and the probability structure of semi-Markov switching signal, the sufficient stability conditions for the considered systems are presented in terms of a set of linear matrix inequalities and a proper semi-Markov switching condition. Based on such conditions, the time delay and mode dependent controller can be designed to stabilize the corresponding closed-loop systems. Finally, two examples are given to illustrate the effectiveness of our results.