Delay-dependent stability analysis and controller synthesis for Markovian jump systems with state and input delays

This paper focuses on the problem of delay-dependent robust stochastic stability analysis and controller synthesis for Markovian jump systems with state and input delays. It is assumed that the delays are constant and unknown, but their upper bounds are known. By constructing a new Lyapunov–Krasovskii functional and introducing some appropriate slack matrices, new delay-dependent stochastic stability and stabilization conditions are proposed by means of linear matrix inequalities (LMIs). An important feature of the results proposed here is that all the robust stability and stabilization conditions are dependent on the upper bound of the delays. Memoryless state feedback controllers are designed such that the closed-loop system is robustly stochastically stable. Some numerical examples are provided to illustrate the effectiveness of the proposed method.