Robust H_∞Control And Filtering Of Stochastic Time-Delay Systems

It is well known that time-delays, parameter uncertainties and stochastic perturbation are frequently encountered in various practical and engineering fields. These factors are usually the source of instability and degradation in control systems. Therefore, one has to consider the effect of time-delays, parameter uncertainties and stochastic perturbation when modeling the systems. Plentiful results have been reported on control theory for stochastic delayed system, however, there remain many open but challenging problems.Based on the knowledge of stochastic analysis and Lyapunov-Krasovskii functional the-ory, by linear matrix inequality technique etc., this thesis focuses on stability analysis, robust control and filtering problem for several kinds of stochastic time-delay systems. The main results obtained in this thesis are as follows:1. The problem of robust mixed H2/H∞guaranteed-cost control for uncertain neu-tral stochastic distributed time-delay systems (UNSDDS) is investigated. By Ito formulation, cross-terms bounding technique, Jensen inequality, Gronwall-Bellman inequality and LMI ap-proach etc., Lyapunov-Krasovskii functionals are constructed to establish a linear stochastic bounded real lemma, by which delay-dependent conditions for the solvability of the robust mixed H2/H∞guaranteed-cost control problem are proposed, and the robust mixed H2/H∞guaranteed-cost controllers are designed to guarantee the loop systems are mean-square expo-nentially stable for all admissible uncertainties with zero disturbance input. The time-varying delays considered include neutral delay, discrete delay and distributed delay, which may be equal to each other or not. Numerical examples are presented to show the effectiveness of the results and very the H2、H∞performances.2. By Ito formulation, cross-terms bounding technique, Jensen inequality, Gronwall-Bellman inequality and LMI approach etc., Lyapunov-Krasovskii functionals are construct-ed and free-weighting matrices are introduced to study robust H2/H∞filtering problems for uncertain stochastic time-delay systems (USDS) and uncertain neutral stochastic distributed time-delay systems. According to Hamilton-Jacoby-Issac condition, complete square method is applied to derive linear stochastic bounded real lemmas for uncertain stochastic time-delay systems, by which delay-dependent conditions for the solvability of the robust H2/H∞filter-ing problems are proposed, and the robust H2/H∞filters are designed to guarantee the filtering error systems are globally asymptotically stable in probability for all admissible uncertainties with zero disturbance input. Based on linear stochastic bounded real lemmas for uncertain s-tochastic time-delay systems established for uncertain neutral stochastic distributed time-delay systems, delay-dependent conditions for the solvability of the robust H2/H∞filtering problems are proposed, and the robust H2/H∞filters are designed to guarantee the filtering error systems are mean-square exponentially stable for all admissible uncertainties with zero disturbance in-put. The delays considered are interval time-varying, and the restriction that the upper bound of the delay derivative is less than1is removed by introducing free-weighting matrices. The new Lyapunov-Krasovskii functional takes into account the information of the time-varying delay, the upper and lower bounds of the time-varying delay. Numerical examples are given to illustrate the effectiveness of the results.3. The delay-dependent mean-square exponential stability problems of uncertain neu-tral stochastic distributed time-delay systems and uncertain stochastic time-delay systems are investigated. By Ito formulation, cross-terms bounding technique, Jensen inequality, Gronwall-Bellman inequality and LMI approach etc., Lyapunov-Krasovskii functionals are constructed and free-weighting matrices are introduced to obtain delay-dependent mean-square exponential stability condition for uncertain neutral stochastic distributed time-delay systems. Numerical examples are proposed to show that the results improve some existing ones. By Lyapunov-Krasovskii theory and LMI method, under the generalized Finsler lemma (GFL) framework, delay-dependent mean-square exponential stability criteria are established without involving any model transformation, Jensen inequality or additional free-weighting matrix. Moreover, GFL is also employed to obtain stability criteria for a class of uncertain linear stochastic neu-tral systems with different discrete and neutral delays. Numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing ones. The delays considered are interval time-varying, and the restriction that the upper bound of the delay derivative is less than1is removed by introducing free-weighting matrices or applying GFL. The new Lyapunov-Krasovskii functional takes into account the information of the time-varying delay, the upper and lower bounds of the time-varying delay.4. The problems of robust H∞dynamic output feedback control and filtering for uncer-tain I to-type stochastic Markovian jump systems with unknown nonlinearities satisfying lin-ear Lipchiz growth condition and interval mode-dependent time-varying delays is investigated. The aim of this problem is to design a Markovian jump exponential filter such that the filtering error system is robustly stochastically exponentially mean-square stable for a prescribed H∞disturbance attenuation level. By Lyapunov-Krasovskii theory and generalized Finsler lemma (GFL), novel delay-range-dependent and delay-derivative-dependent sufficient conditions are obtained to guarantee the existence of desired exponential Hx filter, which can be constructed by solving simultaneous Linear matrix inequalities (LMIs). Neither model transformations nor free-weighting matrices are involved, therefore, conservatism and computation burden result from them can be avoided. Furthermore, the usual assumption that the derivatives of the time-varying delays are less than1is removed due to the applying of GFL. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.5. The robust mixed H2/H∞global linearization filtering problem for a general nonlin-ear stochastic system with interval time-varying delay and exogenous disturbance is studied. For a general nonlinear stochastic system with exogenous disturbance, although the robust H∞filter can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality (HJI), it is difficult to solve the second-order nonlinear HJI except those special cases. Based on the global linearization scheme and Lyapunov-Krasovskii functional theory, a stochastic bounded real lemma is established, by which the robust H∞global linearization filter design for the non-linear stochastic time-varying delay system is proposed via solving simultaneous linear matrix inequalities (LMIs) associated with the filtering problem in linear stochastic time-varying delay systems at vertices instead of solving the HJI associated with the H∞filtering problem in the nonlinear stochastic time-varying delay system. When the worst case disturbance attenuation of H∞filtering is considered, the mixed H2/H∞filter design problem is also solved from the H2suboptimal estimation point of view. A simulation example is provided to illustrate the effectiveness of the proposed method.Finally, the conclusions are summarized and the directions of future studies are proposed.