Output Feedback Control Design Of Interval Type-2 Fuzzy Systems

There are many nonlinear phenomena in real world that are difficult to describe with linear models.The T–S fuzzy model was proposed in this case by Tagaki and Sugeno.The T–S fuzzy model can infinitely approximate the nonlinear model of the systems,and it is described in terms of the IF–THEN fuzzy rule whose represents the local lin-ear input–output relationship of the nonlinear system.Its chief characteristic is to use a linear system model to represent the local dynamics of each fuzzy rule,and the original nonlinear systems can be approximated by blending these linear models via a set of mem-bership functions.The interval type-2 fuzzy models not only can handle the uncertainties of membership functions involved in type-1 fuzzy sets,but also can reduce the burden of computation for type-2 fuzzy models.Stochastic systems can describe the effect of phenomena of some random interference or abrupt structural changes on system states in real world,its research has attracted much attention in the field of control.Based on the existing work,the problems of stability analysis as well as output feed-back controller design are investigated for interval type–2 fuzzy systems.The main con-tributions of this dissertation are summarized as follows:1)The problems of extended dissipative output feedback controller design for interval type-2 fuzzy systems are studied by using line integral Lyapunov function method.Based on line integral Lyapunov theory,the asymptotic stability and extended dissipativity of the closed-loop system are proved in the framework of fuzzy systems.On this basis,L₂-L_∞performance,H_∞performance,passive performance and dissipative performance can be studied in a unified framework,and the sufficient condition obtained is more general than the one which is based on common quadratic Lyapunov function.By Finsler’s lemma,the nonlinear coupling problem is solved for controller parameter matrix and Lyapunov matrix in dynamic output feedback design,and a sufficient condition for linear form is established.2)The problems of the stochastic admissibility,H_∞performance analysis and static output feedback controller design are studied for a class of continuous-time It（?） stochastic Markovian jump singular systems with time-varying transition rate by using stochastic Lyapunov function.A sufficient condition of stochastic admissibility and H_∞perfor-mance of the closed-loop systems under consideration is established.However,the suf-ficient condition is nonlinear with respect to some matrix variables.In light of Finsler’s lemma,this nonlinear condition can be transformed into linear one,based on which the output feedback controller can be developed.3)The problems of stability and H_∞performance analysis as well as dynamical out-put feedback controller design for a class of It（?） stochastic interval type-2 fuzzy systems are studied.In terms of line integral Lyapunov function approach,a sufficient condition of stochastic asymptotic stability and H_∞performance is established for the system under consideration.This condition has less conservative than the one obtained by quadratic Lyapunov function method.The sufficient condition is of nonlinear form with respect to some matrix variables.Transforming nonlinear matrix inequalities into linear matrix inequality,the dynamic output feedback controller is developed in terms of Finsler’s lem-ma.