Stability Analysis And Controller Design Of T-S Fuzzy System

T-S fuzzy model has gradually become an indispensable tool in the study of complex nonlinear systems.It can combine mathematical theory with fuzzy logic theory,accurately approximate nonlinear systems,and make full use of linear system theory and its advantages.In addition,the non-fragile controller can change the parameters of the controller in some cases,the stability condition of the system can be obtained better.And the sampled-data controller can make the discrete-time digital control signal remain unchanged in the sampling interval,and can only change at each sampling time,so as to achieve the purpose of low cost and high reliability.Therefore,this paper will mainly study the stability of T-S fuzzy system,through the design of non-fragile controller and sampled-data controller to analyze the performance of the system.And the feasibility of the control method are verified by numerical examples.The main contents of this paper are as follows:Firstly,for T-S fuzzy systems with time-varying delays and uncertainties,a non-fragile controller is designed.The finite-time stability and extended dissipative performance of T-S fuzzy systems are analyzed.By constructing an augmented Lyapunov-Krasovskii function,using the reciprocally convex matrix inequality,integration by parts,linear matrix inequalities(LMIs)and other methods,a new finite-time bounded with extended dissipative condition can be obtained.Finally,a numerical example is given to illustrate the feasibility of the the control method.Secondly,for T-S fuzzy systems with time-varying delays and uncertainties,a nonfragile memory sampled-data controller is designed,which includes a constant signal transmission delay.Combining with the Lyapunov-Krasovskii function theory,a new criterion of mixed H? and passivity can be obtained.A numerical example show the feasibility of the control method.Finally,for T-S fuzzy systems with time-varying delays and uncertainties,a non-fragile sampled-data controller is designed.The exponential stability and H? performance are analyzed.And a new delay dependent stability criterion is obtained.Two numerical examples are given to illustrate the effectiveness and feasibility of the control method.