Observer-Based SMC for Discrete Interval Type-2 Fuzzy Semi-Markov Jump Models

This study is devoted to the observer-based sliding mode control (SMC) for discrete nonlinear semi-Markov jump models with incomplete sojourn information and application to the quarter-car suspension model. The nonlinear plant with parameter uncertainty is represented by an interval type-2 fuzzy model, where the membership functions of the fuzzy rules are related to the system mode. Since sojourn information is challenging to obtain in practice, the sojourn time probability density function is considered to be incompletely available. The considered system is more general, not only relaxing the traditional assumption that all the sojourn time probability density functions are completely available, but also covering completely available sojourn time probability density functions as a special case. The main innovation is that an observer-based SMC scheme is designed, which makes the discrete nonlinear models have better dynamic performance, and realizes the reachability of discrete quasi-sliding mode. By the interval type-2 fuzzy and classical Lyapunov function, the mean-square stability criterion of the semi-Markov jump models is constructed employing additional matrix variables. Then, an observer-based SMC mechanism is constructed to achieve the reachability of the quasi-sliding mode. Ultimately, the proposed method is validated by a two-degree-freedom quarter-car suspension model.