Composite anti-disturbance control for semi- Markovian jump systems with time-varying delay and generally uncertain transition rates via disturbance observer

The problem of composite anti-disturbance control for semi-Markovian jump systems (S-MJSs) with time-varying delay via disturbance observer is analysed in this study. Unlike the existing methods, generally uncertain transition rates, timevarying delay, multiple disturbances, the H∞ performance and disturbance-observer-based control (DOBC) are all considered in S-MJSs. The method which combines DOBC and H∞ control is used to guarantee the system performance level of time-varying delay S-MJSs. Firstly, a sufficient condition of stochastic stability in the H∞ performance level for the composite control system is given by using piecewise Lyapunov-Krasovskii functional. Secondly, the optimal value of disturbance suppression level for the system is solved by an optimisation algorithm. Thirdly, variation interval of time-delay has been divided into equal small intervals for reducing the conservatism of the method which addresses the mode-dependent time-delay problem. Furthermore, the composite controller and disturbance observer which satisfy the proposed stability condition are designed to address the composite anti-disturbance control problem of the closed-loop system. Finally, two practical systems are provided to testify the accuracy of research methods.