Stability Analysis And Controller Design Of TS Fuzzy System

In the real production and life,many practical systems often involve nonlinear-ities,time variability and time-delays.It is more difficult to apply the traditional control theory for the stability and control problems of these complex systems.Therefore,it has important significance to research nonlinear time-delay models of these systems.And it is well known that Takagi-Sugeno(T-S)fuzzy models can approximate a nonlinear smooth function to any specified accuracy,and then com-plex nonlinear models can be replaced by simple local linear models.As a result,the relatively mature and perfect linear system theory can be used to analyze and control the nonlinear systems.So,it is much valuable to research the T-S fuzzy-linear time-varying delay models.The purpose of this paper is to study the continuous T-S fuzzy linear systems with time-varying delays.The problems of stability analysis and control of these systems are investigated by employing Lyapunov-Krasovskii stability theory,the parallel distributed compensation method,and linear matrix inequality technique.Firstly,the asymptotic stability problem of continuous T-S fuzzy linear time-varying delay systems is studied.By constructing an appropriate Lyapunov-Krasov-skii functional and applying a variety of inequality methods,convex technique to deal with its derivative,an asymptotic stability criterion in the form of linear ma-trix inequalities is given.Then a simulation is done by the YALMIP Toolbox of MATLAB to verify the effectiveness of the theory results.Secondly,by employing the asymptotic stability criterion that is investigated previously,the state feedback stabilization controller is designed by using the parallel distributed compensation algorithm.Then a simulation is done by the Simulink Toolbox of MATLAB to verify the effectiveness of the theory results.