Disturbance-observer-based control for semi-Markovian jump systems with time-varying delay and generally uncertain transition rate

The analysis result of disturbance-observer-based control (DOBC) for semi-Markovian jump systems (S-MJSs) with time-varying delay and generally uncertain transition rate (TR) is given in this paper. At present, there are still some urgent problems needed to be solved for S-MJSs such that conservative of stability, difficult of obtaining of TR in practical system, and the unexpected transient performance is always inevitable, such as larger overshoots and longer settling time. Unlike the existing methods, the proposed method considers the external disturbance, limitation on domain of control signal, uncertain parameters and time-varying delay in the S-MJSs. The piecewise analysis method for time-varying delay systems is extended to DOBC for S-MJSs. First of all, the sufficient condition of stochastic stability based on S-MJSs with more general TR is derived by piecewise Lyapunov-Krasovskii functional. Then, the disturbance observer is designed for estimating the actual disturbance, and the anti-disturbance controller is designed to deal with the control problem of S-MJSs. Furthermore, the problem of actuator saturation is addressed. Finally, two practical example is employed to testify the correctness of the proposed methods.