Sliding mode control for discrete interval type-2 fuzzy semi-Markov jump models with delay in controller mode switching

The problem of asynchronous sliding mode control (SMC) for discrete nonlinear semi-Markov jump models is investigated by the semi-Markov kernel strategy, where asynchronous mechanism means that there is a one-step delay in the controller mode switching related to the system mode. Unlike traditional T-S fuzzy model, the interval type-2 fuzzy model is applied to represent discrete semi-Markov jump systems with uncertain parameters. The main novelty is to design a suitable asynchronous SMC mechanism for the attainment of the quasi-sliding mode, overcoming the difficulty caused by parameter uncertainties. According to the fuzzy Lyapunov function related to the elapsed time and the current mode, the stability criterion of nonlinear model is developed by additional matrix variables, realizing the σ-error mean-square stability of the underlying augmented system. An appropriate fuzzy asynchronous SMC mechanism is established to achieve the accessibility of the quasi-sliding mode. Finally, a tunnel diode circuit model validates the proposed control algorithm.