Asynchronous Adaptive Fault-Tolerant Sliding-Mode Control for T-S Fuzzy Singular Markovian Jump Systems With Uncertain Transition Rates

In this article, the problem of asynchronous sliding-mode control (SMC) for a class of nonlinear singular Markovian jump systems (SMJSs) with actuator faults and uncertain transition rates (TRs) is investigated. Based on Takagi-Sugeno (T-S) fuzzy models, the nonlinear SMJSs are transformed to a set of local linear SMJSs connected by the so-called IF-THEN rules. The hidden Markov model is employed to demonstrate the nonsynchronization phenomenon of the jump mode between the plant and the designed controller. In combination with SMC and adaptive control techniques, a new asynchronous adaptive SMC scheme is developed, which has the ability to completely compensate for the effects of actuator faults and parameter uncertainties. Sufficient conditions for the stochastic asymptotic admissability of the closed-loop T-S fuzzy SMJSs are derived, and the design scheme for controller gain matrices is presented. The reachability of the sliding surface can be guaranteed by the designed control law. Finally, two examples are provided to illustrate the effectiveness of the proposed new design techniques.