Analysis And Control Of Nonlinear Time-delay Systems Based On T-S Model

The T-S fuzzy model offers a universal framework to represent complex nonlinear systems,dynamic nonlinear systems can be represented as weighted sum of several local linear sub-systems via nonlinear fuzzy weights,and each linear sub-system can effectively describe the local characteristics of the nonlinear systems.With the help of the favourable semi-linear property,perfect analysis and synthesis methods of linear systems can be introduced into the control problem of nonlinear systems via T-S fuzzy model,which provides a powerful method for the control of nonlinear systems.On the other hand,the phenomenon of time delay is inevitable in various practical control systems,the existence of time delay often affects the control performance and may even lead to the instability of the systems,therefore,the stability analysis and controller synthesis of time-delay systems are of great significance for practical engineering applications.In industrial production and practical control systems,time-delay systems are often highly nonlinear.Therefore,it is quite difficult to model and control the time-delay systems directly.T-S fuzzy model can approximate nonlinear systems with arbitrary precision,consequently,the control problem of nonlinear time-delay systems based on T-S fuzzy model has attracted more and more attention,and many plentiful results have been achieved.In this dissertation,based on membership-function-dependent(MFD)analysis method,considering the information of the membership functions,less conservative stability conditions are derived for T-S fuzzy time-delay systems by constructing appropriate Lyapunov-Krasovskii(L-K)functional and employing integral inequality technique together with reciprocally convex combination approach.Fuzzy state feedback and static output feedback controllers are presented under the imperfect premise matching(IPM)design scheme,which are different from the traditional parallel distributed compensation(PDC)controllers,the membership functions and the number of fuzzy rules of the fuzzy controllers can be selected flexibly.By selecting a smaller number of fuzzy rules and choosing some simpler membership functions to replace the complex ones in the fuzzy models,the flexibility of the controller design is increased,and the complexity and the implementation cost of the controllers are reduced.This dissertation is organized as follows:(1)Based on the global boundary information of membership functions,the analysis and control of fuzzy constant time delay systems are investigated.Firstly,and then the membership-function-independent(MFI)stability conditions are obtained by constructing a simple L-K functional.Secondly,fuzzy memory state feedback controllers are designed under the IMP design technique,the membership functions of the memory controllers can be selected freely,and then the flexibility of the controller design is increased;the global upper and lower bound information of the membership functions is considered to reduce the conservatism of the design conditions,and then the less conservative stabilization conditions are obtained.(2)Based on piecewise boundary information of membership functions,the analysis and control of fuzzy constant time delay systems are considered.Firstly,some piecewise membership functions represented by convex combination of local upper and lower bounds of subspaces are constructed to approximate the original membership functions,meanwhile,the boundary and shape information of membership functions is considered adequately.Furthermore,more relaxed MFD stability results are obtained by employing the free-matrix-based integral inequality.Secondly,IPM-based state feedback controllers are proposed,the membership functions and the number of fuzzy rules of the fuzzy controllers can be freely selected to enhance the design flexibility.(3)The stability and stabilization control for T-S fuzzy systems with state and input delays are investigated under the MFD analysis method.Firstly,the local boundary information of membership functions is considered under the MFD method.Moreover,the auxiliary function-based integral inequality and a recently developed double integral inequality are selected to deal with the integral term,and less conservative MFD stability conditions are obtained by constructing an augmented L-K functional with triangle integral.Secondly,IPM-based state feedback controllers are presented for T-S fuzzy systems with state and input delays,the membership functions and the number of fuzzy rules of the fuzzy controllers can be selected flexibly.(4)The MFD analysis and state feedback control for T-S fuzzy systems with time-varying delays are considered.A new augmented L-K functional is constructed by introducing some double delay integral terms into the augmented vectors.In addition,some piecewise membership functions are constructed to approximate the original membership functions,and less conservative MFD stability conditions are obtained by combining with the integral inequality technique and the reciprocally convex combination inequality.Secondly,IPM-based state feedback controllers are presented by employing the Finsler lemma,the fuzzy controllers are not required to share the same membership functions and the same number of fuzzy rules with the fuzzy models.(5)New IPM-based static output feedback controllers for fuzzy systems with time-varying delays are investigated.The local boundary information and shape characteristics of membership functions are fully considered in the stability analysis.Meanwhile,combining with Jensen integral inequality and the reciprocally convex combination inequality,less conservative MFD stabilization conditions are obtained by means of linear matrix inequalities(LMIs).The results do not contain equality constraints and there is no rank constraint on output matrix.Furthermore,the membership functions and the number of fuzzy rules can be selected flexibly.