Anti-disturbance control for time-varying delayed semi-Markovian jump systems with saturation and generally uncertain transition rates via disturbance observer

The issue of anti-disturbance control for semi-Markovian jump systems (S-MJSs) with saturation via disturbance observer is investigated in this paper. Compared with the existing results, time-varying delay, actuator saturation, exogenous disturbance and generally uncertain transition rates are all considered in S-MJSs. Firstly, the sufficient condition of stochastic stability based on S-MJSs with time-varying delay is proposed by stochastic Lyapunov–Krasovskii functional. Secondly, disturbance observer-based control is applied in S-MJSs for addressing exogenous disturbance, and the controller is designed to guarantee the system performance. After that, the maximum estimation of domain of attraction is solved by an optimisation problem. Finally, two practical cases are introduced for testifying the accuracy of the proposed methods.