Robust Sliding Mode Control For A Class Of T-S Fuzzy Descriptor Systems With Time-Delay

Singular systems have always been a hot topic at home and abroad.With the development of linear singular systems,researchers have begun to challenge the research field of more complex nonlinear singular systems.The T-S fuzzy descriptor system model combines the nonlinear singular systems theory with the fuzzy theory to solve the control problem of the nonlinear singular systems model,and uses multiple linear singular systems models to approximate or to represent a global nonlinear singular systems model.In addition,time-delay and uncertainty usually exist in the actual systems.Time-delay and uncertainty often lead to instability or poor performance of system.Therefore,the study of time-delay uncertain system is very important both in theory and in practice.The thesis researches the problem of robust sliding mode control for a class of uncertain T-S fuzzy descriptor systems with time-delay.Based on singular system theory and variable structure control theory,delay-dependent sufficient conditions are established and expressed in terms of linear matrix inequalities by constructing appropriate Lyapunov-Krasovskii function,which guarantee the sliding mode dynamics to be admissible.The main research works are as follows:1.For a class of time-delay uncertain T-S fuzzy descriptor systems,the bounds of the nonlinear and uncertain terms exist and are known.Firstly,the integral sliding surface is designed.Secondly,by constructing a Lyapunov-Krasovskii function with some triple integrals,delaydependent sufficient conditions are established to guarantee the system admissibility,and all gain matrices in the sliding surface are determined.Then,an appropriate sliding mode control law is designed so that the system trajectory can reach the specified sliding mode surface and then move along the sliding mode surface.Finally,two numerical examples are given to verify the validity of the theoretical results.2.For a class of time-delay uncertain T-S fuzzy descriptor systems,the bounds of the nonlinear and uncertain terms exist but are unknown.By constructing proper LyapunovKrasovskii function,delay-dependent sufficient conditions are established to guarantee the system admissibility.An adaptive sliding mode control law based on integral sliding surface is designed,and the continuous tanh function with adaptive parameters is used to approximate sign function.In this way,the trajectory of the system can reach the pre-designed sliding surface within limited time and keep moving on the sliding surface thereafter,and the chattering can be effectively suppressed.Finally,the above theories are verified by simulation results.