Anti‐modal‐asynchrony sliding mode control for semi‐Markov jump systems

This article investigates the issue of anti‐modal‐asynchrony sliding mode control (SMC) for discrete semi‐Markov jump systems with bi‐boundary sojourn time. Asynchronous mechanism refers to the mismatch phenomenon between the system mode and the controller mode, in which the modal lag is mode‐dependent to reduce some conservatism compared with traditional mode‐independent lag. In contrast to traditional semi‐Markov jump systems, the sojourn time of each mode in this article is considered to have upper‐and‐lower bounds, representing better characteristics than the upper bound. Based on the semi‐Markov kernel and the Lyapunov function related to the elapsed time of current mode, a sufficient condition is proposed to ensure that the mean‐square stability of the underlying system is achieved under an equivalent SMC mechanism. The conditions for the existence of the designed controller are obtained, which shows that the constructed SMC mechanism is effective against asynchronous mode jumps. An anti‐modal‐asynchrony SMC mechanism is constructed to achieve the reachability of discrete quasi‐sliding mode. Finally, the F‐404 aircraft engine model is given to validate the effectiveness of the control strategy.