Analysis And Design For T-S Model Based Nonlinear Systems With Time-Delays

This paper deals with the stability analysis, filter and controller design problems for aclass of nonlinear systems with time-delays. This kind of nonlinear systems is represented byTakagi-Sugeno (T-S) model fuzzy systems. Specifically, the result mainly contains the followingthree parts:In the first part, theβ?exponential stability and stabilization problems for a class of T-Smodel based neutral systems has been investigated. To solve these problems, new Lyapunov-Krasovskii functional candidates for this class of systems can be chosen by using delay decom-position approach and introducing some exponential functions into corresponding integrands.β-exponential stability conditions of the T-S model based neutral systems are established byusing the Lyapunov-Krasovskii functional and a modification integral inequality. An LMI-basedstate feedback controller design strategy for this class of systems is proposed based on one oftheβ-exponential stability conditions. Two numerical examples are also provided to illustratethe effectiveness of the proposed approach.The second part focuses on fuzzy rule dependent H∞filter design for discrete time nonlinearfuzzy systems with time-varying delay. New delay-dependent Lyapunov-Krasovskii functional isused in which di?erent weighted matrices are corresponding to di?erent intervals. The intervalsdepend on the time-varying delay and its lower and upper bounds. Based on this Lyapunov-Krasovskii functional, some new su?cient conditions guaranteeing stability of the system andsatisfying a prescribed H∞performance level are derived. To reduce conservatism, a fuzzy ruledependent filter is designed by using the resulted criteria. Numerical example is provided toillustrate the e?ectiveness of the proposed methods.The third part is concerned with the stability and stabilization problems of stochastic sys-tems with time delays. By using a delay decomposition approach, a novel Lyapunov-Krasovskiifunctional is proposed. Combining with the Ito? formula and isometry property, a new delay-dependent stability criterion for nonlinear delayed stochastic systems is derived in terms oflinear matrix inequalities. Employing the obtained result, a state feedback controller is con- structed to ensure the stability in mean square of the corresponding closed-loop system. Anumerical example is given to verify the e?ectiveness of the design method.