Observer-Based Adaptive Sliding Mode Control for Nonlinear Stochastic Markov Jump Systems via T–S Fuzzy Modeling: Applications to Robot Arm Model

In this article, the issue of sliding mode control for nonlinear stochastic Markovian jump systems with uncertain time-varying delay is investigated. Considering the system state measurements and the state-dependent disturbances are not available for feedback purposes, an observer-based adaptive control strategy is proposed. Based on the decomposition of the input matrices, the state-space representation of the system is turned into a regular form with the aid of T-S fuzzy models first. Then, a fuzzy observer system is constructed, which could be transformed into two lower order subsystems. By choosing a common linear switching surface, on which it also obtains linear sliding mode dynamics in a simple form. Further, an adaptive controller is synthesized relying on the bounded system delay information to ensure the estimated states driven on the predefined sliding surface and remain the sliding motion. Also, the stochastic stability analysis of the sliding mode dynamics is undertaken with two types of transition rates, and an interesting result reveals that the stability for the dynamics with type of uncertain transition rates may cover the completely known type. Finally, a single-link robot arm model is provided to verify the validity of the proposed method.