Adaptive control of t-s fuzzy systems with markov switching parameters through observer-based sliding mode approach

This paper addresses the problem of observer-based adaptive slid-ing mode control (SMC) for nonlinear Markov jump systems (MJSs), using a Takagi-Sugeno (T-S) fuzzy model with the premise variables of fuzzy rules depend on system state. Firstly, an integral sliding surface is designed based on fuzzy observer system; Secondly, sufficient conditions for stochastic stabil-ity and H infinity perturbation attenuate level are provided for the obtained sliding mode dynamics and error systems using linear matrix inequality techniques. Furthermore, an adaptive SMC law is combined with the observed state vari-ables to ensure finite time reachability of the sliding surface. Lastly, the theory is validated with simulations based on a practical example.