Observer-based adaptive sliding mode control for nonlinear Markovian jump systems

This paper investigates the adaptive sliding mode control problem of nonlinear Markovian jump systems (MJSs) with partly unknown transition probabilities. The system state components are not all unmeasured. The specific information of the model uncertainties and bounds of the nonlinear term and disturbance term are unknown in the controller design process. Moreover, any knowledge of the unknown elements existing in the transition matrix is not required. Our attention is mainly focused on designing the observer-based adaptive sliding mode controller for such a complex system. Firstly, an observer is constructed to estimate the system state. Secondly, we design an integral sliding mode surface and observer-based adaptive sliding mode controller such that the MJSs are insensitive to all admissible uncertainties and satisfy the reaching condition. The stochastic stability of the closed-loop system can be guaranteed. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed results.