Disturbance-observer-based control for semi-Markovian jump systems with generally uncertain transition rate and saturation nonlinearity

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This paper deals with the problem of disturbance-observer-based control (DOBC) for semi-Markovian jump systems (S-MJSs) with generally uncertain transition rate (TR) and saturation nonlinearity. Unlike the existing theories, the proposed method considers the external disturbance and saturation nonlinearity in S-MJSs with more general TR. First of all, to study this DOBC problem, the sufficient condition for stochastic stability of the system is derived by the use of Lyapunov–Krasovskii functional. Then, the design methods of the anti-disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed-loop system. Furthermore, the maximum domain of attraction is estimated by solving an optimization iterative algorithm. Finally, two numerical examples are given to prove the correctness of the proposed results.