| The research of fuzzy control theory has always been a hot spot in the field of control,especially the T-S fuzzy model as an effective method to deal with the control problem of complex nonlinear system.Because of its strong robustness,sliding mode variable structure control(SMVSC)is widely used in the control field.Uncertainty and time delay are unavoidable in practical systems,but their existence will adversely affect the performance of the system and even lead to system instability.Therefore,the problem of T-S fuzzy sliding mode variable structure control with time delays and uncertainties is of great research value.In this paper,the study mainly focused on the SMVSC for T-S fuzzy systems with time-delay and uncertainty.The main work is as follows:(1)Sliding mode variable structure control problem of uncertain T-S fuzzy systems with both state delay and input delay is studied.First ly,a sliding mode surface is designed with a sliding mode compensator,and a new sufficient condition for the asymptotic stability of the sliding motion is proposed using LMI technology and Lyapunov stability theory.Then,appropriate sliding mode controller is designed making the state trajectories of the system can be driven to the sliding surface in a finite time,and stay on the sliding surface in the following time.Finally,the feasibility of the theory is verified by a simulation.(2)The problem of uncertain T-S fuzzy sliding mode variable structure control of the system with time delay is studied for Markovian jump systems.Firstly,an appropriate integral sliding mode surface is designed.Then,the sufficient conditions guaranteeing the asymptotic stability of sliding mode is put forward by constructing the Lyapunov function.Then,a sliding mode controller is designed to make the state trajectories of the system can be driven to the sliding surface in a finite time and remain there in the following time;finally,the feasibility of the theory is verified with simulation. |
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