A novel learning-based asynchronous sliding mode control for discrete-time semi-Markov jump systems

In this paper, a novel asynchronous sliding mode-based learning control is proposed for a class of discrete-time semi-Markov jump systems, in which the probability density function of sojourn-time is dependent on two consecutive modes. The asynchronous switching characteristic is employed for the nonsynchronization between the controller and the jump modes. Based on the discrete-time semi-Markov kernel and multiple-Lyapunov functions, sufficient conditions are provided to guarantee the σ -error mean-square stability of the sliding mode dynamics. Furthermore, a recursive sliding mode learning controller is designed such that the sliding modes can be driven onto the designed sliding surface and the chattering caused by the asynchronous switching and mode jump can be effectively suppressed. Finally, numerical simulations on the continuous stirred tank reactor system are given to demonstrate the effectiveness and potential of the proposed techniques.