H_∞ Control For A Class Of Uncertain T-S Fuzzy Descriptor Systems Using Sliding-mode Control

In actual control systems,there are common factors such as uncertain parameters,external disturbance,and nonlinearity and so on.These factors will affect the performance of the system and even cause instability.The method based on T-S fuzzy system modeling has proved to be a universal approximation model,which provides a powerful research tool for nonlinear system.On the other hand,sliding mode control has received a lot of research attention because of its strong robustness to system disturbance and uncertainty,as well as its fast response.In this paper,the design of sliding mode control is carried out for uncertain T-S fuzzy descriptor systems and uncertain T-S fuzzy descriptor time-delay systems.Some groundbreaking results are obtained.The main research work is as follows:(1)Most of T-S fuzzy sliding-mode control approaches require a strict premise assumption,that is,all the subsystems share a common input matrix.This assumption will greatly reduce the applicability of the approach.This paper focuses on removing the premise assumption.For this reason,we put forward a dynamic sliding mode controller to study the T-S fuzzy descriptor system.(2)In order to study the T-S fuzzy descriptor system,we design a new sliding mode function,which is characterized by linear dependence on the system state vector and system control input vector,and this paper proves that the system state can reach the sliding surface in finite time.(3)In this paper,we study the uncertain T-S fuzzy descriptor system.Generally when researching uncertainties in sliding mode control,the uncertain terms satisfies the matching condition.However,in this paper,the uncertain terms do not satisfy the matching condition.Therefore,we adopt the robust H∞ control.(4)By using the Lyapunov stability theory and the linear matrix inequality(LMI)method,the sufficient conditions for the system's admissibility and robust H∞performance are given.Three simulation examples are presented to demonstrate the effectiveness and advantages of our proposed method.