Second Order Sliding Mode Control For T-S Fuzzy Descriptor Systems

Compared with normal systems,descriptor systems are described by a set of differential equations and algebraic equations.It is more natural,convenient and precise to represent some practical systems by descriptor systems.For this reason,the descriptor system plays an irreplaceable role in many systems,such as power system,robot system,biological system,missile system and so on.T-S fuzzy control theory combines fuzzy control with non-fuzzy control.It provides a model foundation for solving nonlinear system control problems,which has become one of the research directions of many scholars.The T-S fuzzy descriptor system combines the descriptor system with the T-S fuzzy system to solve the control problem.Therefore,it has more important academic value and extensive practical application background,and has become a hot research topic at present.In addition,second-order sliding mode control not only has the advantages of traditional sliding mode control,but also has the effect of eliminating chattering.Therefore,the study of second order sliding mode control of T-S fuzzy descriptor system is of deeper significance.Aiming at the uncertain T-S fuzzy descriptor system model,this paper considers the existence of parameter uncertainty,time delay and external interference in the system,and studies the stability of the system with the help of sliding mode control theory,descriptor system theory and stability theory.The main research work is as follows:1.The model of T-S fuzzy descriptor system is studied,and the stability of the system is analyzed under the condition that the hypothesis is satisfied.First,a sliding surface is designed,and a sufficient condition is obtained to make the sliding mode regular,impulse and stable.Then,a sliding controller is designed to meet the arrival conditions.Finally,simulation results are given to verify the validity of the conclusions.2.The model of time-delay uncertain T-S fuzzy descriptor system is studied,a new sliding surface is designed and a second order sliding mode controller is designed.Firstly,an integral sliding surface with time delay gain is designed,and a linear matrix inequality related to delay is obtained by analyzing sliding mode.Secondly,a second-order sliding mode controller is designed,so that the system state reaches the sliding mode surface.Finally,the above theory is verified through simulation results.3.The robust dissipation control of time-delay uncertain T-S fuzzy descriptor systems is studied.Firstly,the admissibility of time-delay uncertain T-S fuzzy descriptor system and the strict dissipation under a dissipation index are discussed.Finally,a numerical simulation result are given to verify the validity of the conclusions...