Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities

This paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems (MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional (LKF), utilizing the properties that the sum of each row is one in a transition probability matrix and some tractable linear matrix inequalities (LMI), a sufficient condition is established such that the system under consideration is stochastically stable. Second, the design method of time-delay-dependent state feedback controller is proposed to ensure that the resulting closed-loop system is stochastically stable. Since no free matrix variables are applied under the proposed conditions, the method proposed reduce the complexity of calculations. Finally, two simulation examples are presented to show the effectiveness of the proposed method. Compared with the existing literature, in the proposed method not only the conservatism is reduced under the derived stability and stabilization conditions, but also the total number of matrix inequalities is less.

Automated summary

This paper investigates state feedback controller design for discrete-time Markovian jump systems with time delay and two Markov chains, proposing an improved Lyapunov-Krasovskii functional and a time-delay-dependent state feedback controller design method to reduce complexity in calculations. Two simulation examples are presented to demonstrate the effectiveness of the proposed method, which reduces conservatism and the total number of matrix inequalities compared to existing literature.