| T-S fuzzy model is a global model formed by a weighted sum of several linear submodels via nonlinear fuzzy weights,and can approximate any smooth nonlinear functions to any specified precision within any convex compact sets.T-S fuzzy model has provided a powerful method for analysis and synthesis of nonlinear systems because of the fact that it can incorporate the fruitful linear system theory and the flexible fuzzy logic theory into a unified framework to approximate a wide class of complex nonlinear systems.On the other hand,the phenomenon of time-delay is unavoidably encountered in various dynamic systems,and the existence of time-delay is often a source of poor control performance and even instability for the dynamic systems.Therefore,stability analysis and control synthesis of TS fuzzy time-delay systems are of great importance for practical engineering applications.Up to now,most of the existing results regarding stability analysis of T-S fuzzy time-delay systems have focused on Lyapunov asymptotic stability,which is defined over an infinite time interval.However,in many practical applications,the main concern may be the state of dynamical system does not exceed a certain bound during a prescribed finite-time interval,namely finite-time boundedness.There have been only a few results on finite-time boundedness and finite-time stabilization of T-S fuzzy time-delay systems until now.In this dissertation,based on membership-function-independent(MFI)analysis method and membershipfunction-dependent(MFD)analysis method,considering fully the information of time-delays and the membership functions,Lyapunov asymptotic stability analysis,finite-time boundedness analysis and controller synthesis for T-S fuzzy time-delay systems are studied by constructing appropriate Lyapunov-Krasovskii(L-K)functionals and applying integral inequality approach together with the reciprocally convex combination technique.This dissertation is organized as follows:1.Lyapunov stability analysis and control problem of a class of continuous-time T-S fuzzy systems with time-varying delay are studied.Firstly,a new augmented L-K functional with a triangle integral is constructed base on the adequate information of time-varying delay,the auxiliary function-based integral inequalities and the reciprocally convex combination technique are employed to estimate the integral terms in the derivative of L-K functional,then a less conservative delay-dependent stability criterion is derived for T-S fuzzy systems with time-varying delay.Secondly,based on the parallel distributed compensation(PDC)scheme and Finsler lemma,a state feedback controller is designed in the form of linear matrix inequalities for T-S fuzzy systems with time-varying delay.2.Lyapunov stability analysis and stabilization problem of a class of T-S fuzzy systems with two additive time-varying delays are investigated.Firstly,the piecewise membership functions formed by the convex combination of local upper and lower bounds of state subspaces are constructed to approximate the original membership functions,meanwhile,the local boundary information of membership functions is considered adequately.Furthermore,the free-matrix-based integral inequality and the auxiliary function-based integral inequalities are applied to deal with the integral terms in the derivative of L-K functional,then a novel membership-function-dependent asymptotic stability criterion is proposed for T-S fuzzy systems with two additive time-varying delays.Secondly,based on the imperfect premise matching(IPM)scheme,a fuzzy state feedback controller is developed for T-S fuzzy systems with two additive time-varying delays.3.Finite-time boundness analysis and finite-time control of a class of T-S fuzzy systems with constant time delay and exogenous disturbance are investigated.Firstly,a novel augmented L-K functional with a triangle integral is constructed based on adequate information of state time delay,the auxiliary function-based integral inequalities and the free-matrix-based integral inequality are employed to address the integral terms in the derivative of the augmented L-K functional,then a new delay-dependent finite-time boundedness criterion is presented for the considered T-S fuzzy system with constant time delay.Secondly,based on the PDC scheme,a novel fuzzy state feedback controller is designed,which can ensure that the state of the closed-loop T-S fuzzy time-delay system does not exceed a certain bound during a prescribed finite-time interval.4.Finite-time boundness analysis and finite-time control of a class of T-S fuzzy systems with time-varying delay and exogenous disturbance are studied.Firstly,an augmented L-K functional with a triangle integral is established based on enough information of time-varying delay,the improved reciprocally convex combination technique and the auxiliary functionbased integral inequalities are applied to evaluate the integral terms in the derivative of the augmented L-K functional,then a novel delay-dependent finite-time boundedness criterion is established for T-S fuzzy systems with time-varying delay.Secondly,based on the PDC scheme and Finsler lemma,a memory state feedback controller is developed to guarantee the finite-time boundness of the closed-loop T-S fuzzy system with time-varying delay.5.Membership-function-dependent finite-time boundness analysis and finite-time control of a class of T-S fuzzy systems with time-varying delay are investigated.Firstly,the piecewise membership functions are established to approximate the primary membership functions,meanwhile,the local boundary information of the original membership functions is considered adequately.Furthermore,the auxiliary function-based integral inequalities and a relaxed integral inequality are employed to deal with the integral terms in the derivative of the constructed augmented L-K functional and several appropriate slack matrices are introduced,then a new less conservative membership-function-dependent finite-time boundedness criterion is derived for the considered T-S fuzzy system with time-varying delay.Secondly,based on the IPM scheme,a fuzzy state feedback controller is designed to ensure finite-time boundness of the closed-loop T-S fuzzy system with time-varying delay,which can be obtained by solving a set of linear matrix inequalities.The membership functions and the number of fuzzy rules of the developed fuzzy controllers can be freely chosen,which greatly enhances the flexibility of controller design. |
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