Observer-based SMC for discrete semi-Markov switching models

This study focuses on the observer-based sliding mode control (SMC) for discrete stochastic switching models, where the semi-Markov kernel information is incomplete. Because the sensors do not always have direct access to the state vector in a complex environment, an observer-based output measurement is considered to estimate the system state. In contrast to previous works, the observer-based strategy is first investigated in studying the SMC for semi-Markov switching systems under the discrete framework. The sufficient condition for achieving mean-square stability is proposed to solve the desired observer and controller gains by utilizing the upper bound of sojourn time, along with the Lyapunov function that pertains to the system mode and the elapsed time. A mode-dependent SMC law is also constructed to ensure that the system state can reach the specified sliding region. Finally, the efficiency of the proposed method is demonstrated through the single-link robot arm model.