Stability Analysis And Controller Design For Class Of T-S Fuzzy Systems With Time Delay

The phenomena of time-delays are often encountered in dynamic systems,such as aircraft dynamics,communication systems and so on.These delays are usually time-varying,and have an adverse impact not only on the system performance but also on its stability.Therefore,neglecting the effects of delay in the analysis may led to instability and disastrous consequences.On the other hand,fuzzy systems in the form of the Takagi-Sugeno(T-S)model have attracted great interests.It has shown that the T-S model method can give an effective way to represent complex nonlinear systems by some simple local linear dynamic systems with their linguistic description.And some nonlinear dynamic systems can be approximated by the overall linear T-S fuzzy models for the purposes of stability analysis and controller design.Therefore,stability analysis for T-S fuzzy systems with time-varying delay has attracted much attentions.At present,a great number of stability criteria have been reported.However,there is room for further improvement in stability analysis of T-S fuzzy systems with time-varying delay.Based on the T-S fuzzy model,this paper investigate the problems of stability analysis,robust stability analysis and H_?controller design of nonlinear time-varying delay systems.The main contents of this paper are as follows:(1)Firstly,the stability of continuous-time T-S fuzzy control systems with time-varying delay is analyzed.Based on the Lyapunov stability theory,a new Lyapunov-Krasovkii(L-K)functional including some triple integral terms and augmented terms is constructed which contains more information of time-varying delays.Then,by using the Jensen inequality,free-weighting matrix method,and convex combination approach,we can obtain a less conservative stability criterion.Besides,aiming at the system with uncertain parameters,the robust stability of this system is studied and improved robust stability criterion is given.Finally,a numerical example is given to illustrate the effectiveness of the proposed.(2)Secondly,for the discrete-time T-S fuzzy systems with time-varying delay,the stability and robust stability of the system are analyzed.When constructing the L-K functioanl,triple summation terms and augmented terms are introduced in L-K in order to obtain a better result.Then,applying the summation inequality,free-weighting matrix method,and convex combination approach,a new delay-dependent stability criterion and a robust stability criterion for T-S fuzzy discrete-time systems with time-varying delay are derived.Finally,by comparing the results in some recent papers,the effectiveness of the proposed stability criterion is verified.(3)In practical application,there are disturbances in the system.In this case,we consider the problem of delay-dependent robust H_? control for uncertain continuous-time and discrete-time T-S fuzzy systems with time-varying delay.Based on the parallel distributed compensation(PDC)scheme,we provide a method to design a H_? controller that ensure the robust stability and a prescriced H_? performance level for the resulting closed-loop systems.A numerical example is given to demonstrate the effectiveness of the method.