Analyses And Synthesis For T-S Fuzzy-model-based Systems With Time-delay Under Imperfect Premise Matching

T-S(Takagi-Sugeno)fuzzy model is a powerful tool to describe fuzzy systems,which can provide a general and systematic framework to represent the nonlinear plant as an average weighted sum of some linear subsystems.Besides,time-delay is quite common in practical control systems,which can greatly destroy the performance of the systems.Therefore,research for T-S fuzzy-model-based systems with time-delay system is playing an essential role in engineering practice.In this paper,we choose T-S fuzzy-model-based system with time-delay as research subject,and we will mainly investigate stability analysis,stabilization analysis and fuzzy H_?filter design issues.The main work and contribution of this paper are given as follows:1.This paper studies the stability analysis issue for nonlinear systems with distributed time-delay.Firstly,the T-S fuzzy model of the nonlinear systems is established.To decrease the conservatism of the results,a novel integral inequality with compact structure is used to analyze the stability conditions.As this integral inequality is tighter than other existing ones,less conservative stability conditions can be obtained.Moreover,by introducing a membership-functions-dependent technique,the stability conditions can be further relaxed.The derived results are presented as LMI-based stability conditions.2.This paper considers the stabilization analysis problem for T-S fuzzy-model-based systems with distributed time-delay under imperfect premise matching conditions.Unlike conventional PDC fuzzy controller design method,the fuzzy controller to be designed is allowed to use different membership functions and different number of fuzzy rules from the T-S fuzzy model.As a result,the drawbacks of the PDC method can be avoided,and greater design flexibility of fuzzy controller can be achieved.Furthermore,a novel integral inequality mentioned above is introduced and the information about the membership functions is considered,which can help reduce the conservatism of the stabilization conditions.3.This paper is concerned with the imperfect premise matching fuzzy H_?filter design issue for T-S fuzzy-model-based systems with time-varying delay.To overcome the limitations of the conventional PDC-based fuzzy H_?filter design method,the fuzzy H_?filter to be designed and the T-S fuzzy model of the filtering system are allowed to use different premise membership functions and different number of fuzzy rules.As a consequence,greater design flexibility can be achieved.Moreover,for the sake of reducing the conservatism of the results,the informationabout the membership functions of the fuzzy model and the fuzzy H_?filter is introduced.Besides,the membership-functions-independent fuzzy H_?filter design method is also given,which has a simple form and is easier to be realized in practice.4.This paper also considers fuzzy H_? filter design problem for T-S fuzzy-model-based systems with time-varying delay,which is based on the PDC methodology.When analyzing stability conditions,a novel integral inequality is used to replace the traditional Leibniz-Newton formula to deal with the integral term in the derivative of the Lyapunov function.As a result,the conservatism of the fuzzy H_?filter can be reduced.Besides,the information about the membership functions is also taken into consideration,which can further relax the results.5.On the basis of the discussion above,this paper investigates imperfect premise matching fuzzy H_?filter design issue for the same T-S fuzzy-model-based systems with time-varying delay.In order to obtain greater design flexibility,the fuzzy H_?filter to be designed is assumed to have different membership functions and different number of fuzzy rules from the fuzzy model.Moreover,when analyzing stability conditions,a novel integral inequality which is mentioned above is also applied to deal with the integral term,and the information about the membership functions of the T-S fuzzy model and fuzzy H_?filter is considered.As a result,less conservative fuzzy H_?filter can be obtained.6.In order to illustrate the effectiveness and superiority of the proposed stability conditions,stabilization conditions and several fuzzyH_? filter design methods,corresponding simulation examples are provided,which includes the comparison with other relative methods presented in other papers and the analyses.