Research On Stabilization And Synchronization Of Delayed Neural Networks Based On Intermittent Control Strategies

Intermittent control has been widely applied to various fields such as com-munication, electronic circuit, biology, and economy due to its many advantages including higher efficiency, lower cost, as well as easy to implementation. Anal-ysis and synthesis of intermittently controlled systems have been intensively in-vestigated in the literature. Most of the results are based on common Lyapunov function/functional methods. Since these methods cannot fully capture the hybrid structural characteristics of the intermittently controlled systems, the resulting stability criteria entail certain conservatism, or they are not suitable to stability analysis of the intermittently controlled stochastic systems and neutral system-s. In order to overcome the weakness of common Lyapunov function/functional methods, this thesis focuses on developing novel piecewise Lyapunov function-al methods for stabilization and synchronization of several kinds of time-delay systems via periodically/aperiodically intermittent control strategies. These time-delay systems include neutral time-delay systems, stochastic time-delay systems, and delayed neural networks. By taking into account the structure features of the considered systems, switching-time-dependent Lyapunov functionals are con-structed. By applying these Lyapunov functionals, novel criteria for intermittent stabilization and intermittent synchronization are derived. The main results are stated as follows.(1) The periodically intermittent stabilization problem of neutral neural net-work with time-varying delay is investigated. First, a stability criterion is obtained by using a piecewise Lyapunov functional direct method. Next, the new stability criterion is derived by applying a descriptor transformation method and a cor-responding piecewise time-varying Lyapunov functional. Based on the obtained stability criteria, two criteria for designing periodically intermittent control law are provided. Finally, numerical examples show that the descriptor transforma-tion method is superior than the direct method.(2) The synchronization problem of delayed neural networks with stochastic disturbance via periodically intermittent control is discussed. Two cases of time delays are considered:fast time-varying delay and slow time-varying delay. For the case one, combining piecewise Lyapunov functional based method with Razu-mikhin technique, a mean square exponential synchronization criterion can be ob-tained which can remove the restriction that control width is larger than the delay bound. For the case two, by developing a piecewise time-varying Lyapunov func-tional, a mean square exponential synchronization criterion is obtained. Based on the established synchronization criteria, the designs of periodically intermittent synchronization control gain matrices are presented in the form of linear matrix inequalities (LMIs).(3) The time-independent stabilization problem of delayed stochastic neu-ral networks via aperiodically intermittent control is studied. By introducing a switched time sequence depended piecewise Lyapunov functional, and combin-ing with convex technique, establish a criterion which can stabilize the studied stochastic delayed neural networks via aperiodically intermittent control. This criterion not only irrespective of the size of the time delay, but also reveals the impact on the designing aperiodically intermittent control law from control width, rest width and stochastic disturbance intensity.