The Study Of Stability Analysis And Design For Fuzzy/Stochastic Delayed Systems

Firstly, this doctoral dissertation studies, respectively, the problems of robust nonfragileH_∞control, robust H_∞filtering, robust reliable guaranteed cost control and robustH_∞dynamic out-put feedback(DOF) control for Takagi-Sugeno(T-S) fuzzy neutralsystems. Secondly, the stability analysis for a class of impulsive stochastic delayed differentialequations and the problem of state-feedback fuzzy control for a class of impulsivestochastic T-S fuzzy delayed systems are investigated, respectively. The dissertation consistsof six parts with eight chapters:Part 1 contributes to the problem of robust non-fragile H_∞control for a class ofuncertain T-S fuzzy neutral systems with linear fractional parametric uncertainties. Bymeans of Lyapunov-Krasovskii functional, the LMI approach and descriptor system approach,the design solution of robust non-fragile H_∞controller is obtained, which ensuresasymptotic stability of the closed-loop system and guarantees a prescribed H_∞performancelevel.Part 2 is to study the problem of robust H_∞filtering for a class of uncertain T-Sfuzzy neutral systems with time-varying delays. On the basis of Lyapunov-Krasovskiifunctional, Barbalat lemma and the LMI approach, a full-order fuzzy H_∞filter is obtained,which ensures asymptotic stability of the filtering error system and guarantees aprescribed H_∞performance level. Moreover, as an application of the theoretical results,the H_∞filter design problem for a neutral-type nonlinear distributed network (long linewith tunnel diod) is discussed.Part 3 is devoted to investigating the problem of robust reliable guaranteed cost controlfor a class of uncertain T-S fuzzy neutral systems. Based on the fact that actuatorsare non-ideal in real control systems, a more practical system model is introduced byuse of the continuous fault model. The design solution of robust reliable guaranteed costcontroller with constraint of quadratic cost function is obtained via Lyapunov-Krasovskiifunctional, the descriptor system approach, the free weighting matrix method and LMIapproach. Furthermore, the minimum upper bound of the cost function can be derived viathe "mincx" optimal algorithm.Part 4 focuses on the problem of robust H_∞dynamic output-feedback (DOF) control for a class of uncertain T-S fuzzy neutral systems. Utilizing Lyapunov-Krasoviskii functional,Barbalat lemma and the LMI approach, a full-order fuzzy DOF controller has beendevised, which ensures the asymptotic stability of the closed-loop system and guaranteesa prescribed H_∞performance level.Part 5 is concerned with the stability analysis for a class of impulsive stochasticdifferential equations with delays. By means of Lyapunov-Krasovskii functional, It(?) formulaand mathematical analysis, new sufficient conditions ensuring mean square stabilityof the impulsive stochastic functional differential equations are obtained. Finally, as anapplication of the theoretical results, the mean square stability of a class of stochastic impulsiveneural networks with delays is discussed.Part 6 investigates the problem of state-feedback fuzzy control for a class of stochasticT-S fuzzy delayed systems with impulsive effects. The time delay is assumed to appearboth in the state and control input. On the base of It(?) formula, Lyapunov-Krasovskiifunctional and the relaxed linear matrix inequality (Relaxed LMI) approach, the designsolution of state-feedback fuzzy controller is proposed in terms of LMIs such that theresulting closed-loop system is exponentially stable in the mean square.At the end of this dissertation, the results are summarized and further research problemsare pointed out.