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 sliding 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 stability and $ H_{\infty} $ 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 variables to ensure finite time reachability of the sliding surface. Lastly, the theory is validated with simulations based on a practical example.