Stability Analysis And Controler Design For A Class Of Time-Delayed T-S Fuzzy System:A Gaussian-Based Delay Partitioning Approach

With the development of automatic control technology,related researches such as robots,unmanned aerial vehicle,and unmanned driving have received much attention in recent years,all of which requires high control accuracy.In the control system,the delay-dependent control system is always an important research topic.The time-delay exists in any physical system,which has a significant impact on the performance of the system,sometimes even causing system unstable.Time-delay in systems can be classified as constant delay and time-varying delay.For time-varying delays,the traditional analyzing methods are no longer feasible.L-K(Lyapunov-Krasovskii)functional and L-R(Lyapunov-Razumikhin)fuction analysis methods have become the main research ones to analyze the stability of systems with time-varying delays.Substantial works have been done and lots of valuable results were reached based on them.The control of nonlinear systems is always a difficult problem and the emergence of fuzzy control theory is of great significance for nonlinear control.However,due to lack of mathematical descriptions,the late development of the early Madamni fuzzy model is very limited.The emergence of the T-S fuzzy model showed a way to solving this problem by decomposing the nonlinear system into a set of linear subsystems which descriped in a state space form.Based on the abundant research results of the state space theory,the T-S fuzzy model has greatly promoted the development of nonlinear systems.The object studied in this thesis is a class of nonlinear systems with interval time-varying delays based on T-S fuzzy control model.Based on the profound research results of previous scholars,the following aspects were studied:(1)Based on the T-S fuzzy control model,a system model of nonlinear systems with interval time-varying delay was constructed.Based on the Lyapunov-Krasovskii(L-K)stability theory,by utlizing some tighter bounding integral inequalities proposed in recent years,such as Peng-Park integral inequality and Han's integral inequality,a newly constructed L-K functional was given,and the stabilities of a class of T-S fuzzy systems with parallel distributed compensation(PDC)controllers and T-S fuzzy controll systems with parameter uncertainty were analized.(2)Based on the time-delay partitioning technique,which was published by the French scholar Gouaisaut in 2006 and later improved by Cao.et al,this thesis used a Gaussian-distribution-based method to dividing the time-delay interval,and used this to analyzing the stability and designing controllers of a class of T-S fuzzy system with interval time-varying delays,and the numerical analysis results were given in the end.(3)Based on the stability analysis,this thesis also did some efforts on fuzzy controller design.Based on the stability criteria studied above,this thesis has designed a PDC controller for a class of T-S fuzzy control systems with interval time-varying delays,and a robust PDC controller for a class of T-S fuzzy systems with interval time-varying delays and parameter uncertainties.Numerical examples were given in the end.