Robust adaptive control for a class of T-S Fuzzy nonlinear systems with discontinuous multiple uncertainties and abruptly changing actuator faults

In the complex environment, the suddenly changing structural parameters and abrupt actuator failures are often encountered, and the negligence or unproper handling method may induce undesired or unacceptable results. In this paper, taking the suddenly changing structural parameters and abrupt actuator failures into consideration, we focus on the robust adaptive control design for a class of heterogeneous Takagi-Sugeno (T-S) fuzzy nonlinear systems subjected to discontinuous multiple uncertainties. The key point is that the switch modes not only vary with the system time but also vary with the system states, and the intrinsic heterogeneous characteristics make it difficult to design stable controllers. Firstly, the concepts of differential inclusion are introduced to describe the heterogeneous fuzzy systems. Meanwhile, a fundamental lemma is provided to demonstrate the criteria of the boundness for a Filippov solution. Then, by using the set-valued Lie derivative of the Lyapunov function and introducing a vector of specific continuous functions, the closed-loop T-S fuzzy differential inclusion systems are proved to be ultimately bounded. The sufficient conditions for system stability are derived in term of linear matrix inequalities (LMIs), which can be solved directly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control algorithm.