Research On Stability Of Stochastic Neutral System With Distributed Delays

Many problems in the field of industrial technology, socio-economic andbio-engineering, and its dynamic law can be described by a deterministic modeland a stochastic model. In a ideal situation, the system is often represented as adeterministic model. However, new phenomenon in random system is differentfrom that in deterministic system due to stochastic distribute. Moreover, in realisticsystem, due to transmission, measurement etc, time-delay is universal phenomenon,which can make a system instable.Many systems are neutral system with delays, such as population ecology, thenatural model of voltage and current fluctuations in transmission line, automaticcontrol, heat exchangers, and so on. Distributed delays are widely present inrealistic systems, such as the moving image processing, associative memory,thermal processing. The distributed delay can represent the nature of a systembetter. However, stochastic stability on stochastic neutral system with distributeddelays has been not investigated completely， especially for nondeterministicstochastic neutral system with delays which exist in state items, control items, state of thedifferential items, external interference items and evaluation input items. Since then, thisproblem has extensive research value and new problems are to be solved in theory.In this thesis, three problems on stochastic neutral system with distributeddelays are investigated:a) We investigate the mean-square exponential stability of stochastic neutralsystems with distributed delays. By linear matrix inequality approach and themethod of Liapunov functional, a sufficient condition for mean-square exponentialstability of stochastic neutral systems with distributed delays is presented.b) On this part, the stochastically asymptotically stable of uncertainstochastic neutral system with discrete delays and distributed time-varying delay atthe same time has been considered. The sufficient condition is presented based onthe Lyapunov stability theory and differential rule.c) For the uncertain stochastic neutral systems with distributed delays, itscharacteristic is time-varying not only lie in the state of the differential term butalso in the state term and control term. And the parametric uncertainties arenorm-bounded. By designing a state feedback controller, we obtain adelay-dependent criterion such that the resulting closed-loop system is robustly stochastically asymptotically stable.In this paper, the results are based on LMI approach, and numerical examplesshow the feasibility of the method.In sum, some new results of stability problems of stochastic neutral system withdistributed delays have been made, but are not perfect. Based on the conclusion,some problems have been raised to be further studied and explored in this paper.