Research On Stability Analysis And Control For T-S Fuzzy Systems With Time Delay

In practical application,a large number of industrial systems suffer serious nonlinear characteristics,which cause formidable obstacles for analyzing systems.T-S fuzzy models have shown excellent performance in approximation of nonlinear systems to any accuracy via combination of flexible fuzzy logic theory and mature linear system theory,and have been widely applied in aerospace,pattern recognition,power system,robot control,etc.Therefore,the study of T-S fuzzy systems with time-varying delay is of great practical value and theoretical significance.Moreover,time delay is a widespread phenomenon in control systems.The existence of time delays will lead to the degradation of the control performance of the systems,or even the loss of the stability of the original stable systems.Therefore,the time delay must be considered in the process of system analysis.Based on the existing work,the problem of stability analysis and control for T-S fuzzy systems with time delay is investigated.The main contents of this article are as follows:1.The problem of stability analysis of T-S fuzzy systems with time-varying delay is investigated.First,base on the existing reciprocally convex inequality,a new delay-dependent reciprocally convex inequality is proposed in this paper.Second,based on the existing Lyapunov-Krasovskii(L-K)functionals,a novel augmented L-K functional is proposed by augmenting several new s-dependent integral vectors into L-K functional.Based on the idea of membership function dependent matrix,the membership function dependent functional is introduced in the constructed L-K functional.Finally,stability criteria with less conservatism for the T-S fuzzy systems with time-varying delay are derived combining the new delay-dependent reciprocally convex inequality and the novel L-K functional.2.The problem of stability analysis of T-S fuzzy systems with large time delay is investigated.First,based on switching ideas,the T-S fuzzy system with large time delay is modeled as a switch T-S fuzzy time delay system which contains two subsystems.One of them is the stable subsystem running in the small delay periods,and other is a potentially unstable subsystem running in the large delay periods.Second,an exponential stability condition of the system running in small delay periods and an upper bound condition of the L-K functional of the system running in large delay periods are given.Finally,based on switching techniques,an exponential stability condition of the whole system is presented according to the frequency and duration of the large time delay.3.The problem of controller design of T-S fuzzy systems with time-varying delay is investigated.First,based on the structural characteristics of T-S fuzzy systems and the parallel distributed control strategy,a memoryless fuzzy state feedback controller is given.Then,the issue of stabilization of T-S fuzzy systems with time-varying delay is carried out.A line-integral Lyapunov function is introduced to reduce the conservatism of stabilization criterion.Finally,a relaxed stabilization criterion for T-S fuzzy systems with time-varying delay is presented.