Semi-global exponential stability under sampled-data control by emulation approach for Markov jump systems with hybrid time delays

In this paper, we study the problem of semi-global exponential stability for Markov jump systems with hybrid time delays under sampled-data control. Thereinto, we use the emulation approach to design a sampled-data controller under the suitable fast sampling, and hybrid time delays include discrete time delays and distributed time delays. Considering that the Markov jump is a random process, we introduce a novel definition for the right and upper Dini’s derivative of the Lyapunov functional. Under this definition, the variables on which the Lyapunov functional acts are not required to be solutions of the Markov jump systems. Combining this new definition with the global exponential stability of the continuous-time feedback control systems, some sufficient conditions of the semi-global exponential stability for the Markov jump systems are given, which are closely related to the state transition rate of Markov jump, the initial value range of the considered systems, and the maximum sampling interval of the sampled-data control. Then, the theoretical results are applied into a class of oscillator systems. Finally, a numerical simulation is provided to demonstrate the effectiveness of the main theoretical results.