Research On Exponential Stability In Mean-square For Neutral Stochastic Systems With Mixed Time-delays

Recently, the stability analysis of neutral systems, which have delays in both itsstate and the derivatives of its states, has been widely investigated by manyresearchers. As we all know, time-delay exists widely in automatic control systems,which results in mainly instability and poor performance of systems. Stability is ofimportance to dynamic systems, which is not only the demand of the neutralsystems, but also necessity of the realistic meaning. Therefore, the systems havebeen paid attention more and more in the last few years. Many factors can cause theinstability of systems, for example， stochastic perturbations、 uncertaintiesparameters、the random jumps in systems and so on. Therefore, it is necessary toadd that factors in the neutral systems.According to the control theory, the exponential stability in mean-square forstochastic neutral systems with Markovian jumping parameters and mixedtime-delays is studied in this article. By constructing a new Markovian jumpinglyapunov-krasovskii function, using integral inequalities, the stability condition isderived in terms of LIMS. The main contents are as follows:1. The exponential stability is studied for a class of stochastic neutral system withMarkovian jumping parameters and distributed delays.The jumping parameters areregarded as a continuous-time, continuous state Markov process and delays isrelated to Markov jumping. Based on a new lyapunov-krasovskii functional andstochastic analysis, a new delay stability condition is derived in terms of linearmatrix inequality by using some integral inequalities, which in favor of exponentialstability in mean-square of the neutral systems.A numerical example show that themethod is effective.2. The exponential stability in mean-square of stochastic neutral systems withsaturating actuators and mixed time varying delays is concerned. The stochasticproperty of the Markov process is fully considered in the neutral systems and amode-dependent memoryless saturating state feedback controller is designed. Byutilizing a delay-decomposition, a upper bound of time-delay is obtained. A lessconservative condition to ensuring the exponential stability of the stochastic neutralsystems is derived by using a lyapunov-krasovskii functional on the vertices of the polytopic description of the actuator saturations.Numerical examples demonstratethe effectiveness of this proposed methods.