Robust Stability And Stabilization Of Uncertain It(?) Stochastic Systems With Applications  Posted on:20120506  Degree:Doctor  Type:Dissertation  Country:China  Candidate:Y J Li  Full Text:PDF  GTID:1488303356492914  Subject:Control theory and control engineering  Abstract/Summary:  PDF Full Text Request  Based on LyapunovKrasovskii functional method, by using stochastic Lyapunov stabilitytheory, Ito? formula, linear matrix inequalities, freeweighting matrix method and so on, thisdoctoral dissertation is devoted to the research on the robust mean square exponential stability, almost sure exponential stability, robust feedback stabilization of uncertain Ito? stochasticsystems and the exponential stability of uncertain fuzzy stochastic neural networks. The mainresearch work and contributions of this dissertation are summarized as follows:1. The preface gives an introduction to the related background and the latest progress inthe stability analysis, control and applications of stochastic systems, then some preliminaries,lemma and some concepts of stability for stochastic systems are presented.2. The robust mean square exponential stability for a class of uncertain stochastic systems with timevarying delays is discussed. For a class of uncertain stochastic system withtimevarying delays, the information of both variation range and the distribution probabilityof the time delay are considered. Firstly by translating the distribution probability of the timedelay into parameter matrices of the transferred systems,a new modeling method is proposed.In the established model, the parameter uncertainties are normbounded, the stochastic disturbances are described in term of a Brownian motion, the timevarying delay is characterizedby introducing a stochastic variable which satisfies Bernoulli random binary distribution. Byexploiting an appropriative LyapunovKrasovskii functional, stochastic Lyapunov stability theory and some new analysis techniques, some delaydistributiondependent roust stability forstochastic system with linear and nonlinear stochastic disturbances are discussed. The sufficient conditions for the robust exponential stability are given and derived for the system underall admissible uncertainties. All results are given in the form of Linear Matrix Inequalities,which can be easily solved by some standard numerical packages. One of the important features of the results is that the stability conditions are dependent on the probability distributionof the delay and upper bound of the delay derivative, the upper bound of the delay derivative isallowed to be greater than or equal to 1, the limit of the upper bound of the delay derivative mustbe less than 1 is overcome, two numerical examples are given to illustrate the effectiveness andless conservativeness of the proposed method.3. The robust mean square exponential stability for a class of uncertain stochastic system with impulsive disturbance is studied. By constructing a simple LyapunovKrasovskiifunctional, applying Ito? formula and some inequality techniques, the mean square exponential stability sufficient conditions is given and derived based on LMIs. Then, the almost sure exponential stability for a class of neutral stochastic system with timevarying delay and Markovianjumps are derived by the same method. Numerical examples show the correctness of proposedstability criteria.4. The robust nonfragile feedback controller design problem for a class of uncertainstochastic systems with nonlinear disturbance is investigated. By means of LyapunovKrasovskiifunctional, stochastic Lyapunov stability theory and Ito? formula, the nonfragile feedback controller are designed and obtained, the sufficient conditions which making the closedloop system robustly stable are proposed and proved. Numerical examples and simulation show theeffectiveness of designed controller.5. The robust exponential stability for a class of uncertain neural networks system withnonlinear stochastic disturbances is studied. By applying the stochastic Lyapunov stabilitytheory to the neural networks, using the descriptor model transformation and the freeweightingmatrix method, a sufficient condition which making the system robust exponential stability isderived. Numerical examples have shown the effectiveness and low conservativeness.6. The robust mean square exponential stability problem for a class of uncertain impulsivestochastic neural networks systems with mixed timevarying delays and Markovian jumps isinvestigated. By constructing LyapunovKrasovskii functional and using stochastic Lyapunovstability theory, the delaydependent robust exponential stability sufficient conditions for thesystem is derived in terms of LMIs. The numerical example has shown that whether Markovianjump occurs at the impulsive moment or not, the stability criteria proposed is effective.7. The robust exponential stability for a class of uncertain fuzzy stochastic neural networks systems with mixed timevarying delay is investigated. Based on TakagiSugeno (TS)fuzzy models, a class of uncertain fuzzy stochastic neural networks systems is modeled. Byconstructing LyapunovKrasovskii functional, combing the stochastic stability theory with thefuzzy control theory and robust theory, the novel delaydependent stability sufficient conditionsare derived based on LMIs and some integrated inequality techniques. Example and simulationare provided to show less conservative and the effectiveness of the obtained results.Finally, after the summary of this dissertation, the issues of further investigation are proposed.  Keywords/Search Tags:  Robust stability, timevarying delay, Markovian jump, impulsive, neutral distributed timedelay systems, nonfragile controller, Ito? formula, freeweight matrix, meansquare exponential stability, linear matrix inequalities  PDF Full Text Request  Related items 
 
