Research On Stability For Several Classes Of Stochastic Systems With Mixed Time Delays

Due to sudden changes of the external environment,delays of information transmission and exchange,and interferences of random noise,sudden changes of the parameter and structure of the system,time delays and random phenomena often appear in various practical applications such as power system,financial system,aircraft control system,industrial production system and communication system,and are the main causes of system oscillation and instability.Therefore,studying the stability of stochastic systems with mixed time delays has important theoretical significance and application value,which is also the difficulty of the research.In recent years,the stability analysis of stochastic systems with mixed time delays has received extensive attention from scholars at home and abroad.Among them,the stability of Markov jump systems and stochastic neutral systems is particularly concerned.However,the accurate information of the transition rate matrix and system parameters of the Markov jump systems may not be fully obtained,and the incomplete information may have a great impact on its stability analysis.The neutral behavior and other time delays phenomena are often encountered in the Markov jump systems,which may also have adverse effects on the system index.At the same time,since real nervous systems can produce larger impulse in noise amplitudes,and Levy noise is more suitable to describe the neural response process and the dynamic behavior of nerve cells than Gaussian white noise.On the other hand,the loss of sampling data and the high cost and instability of the continuous-time controllers make how to design an effective control strategy a challenging and major problem.In addition,the complexity of the system not only increases the difficulty of stability analysis,but also increases the conservativeness of the stability conditions obtained by the existing methods.Therefore,the research on the stability of stochastic systems with mixed time delays is a challenge and worthy of further study.As concerned above,in this thesis,for several classes of stochastic systems with mixed time delays,we use Lyapunov method,combined with stochastic analysis,linear matrix inequality,integral inequalities,martingale inequalities,and non-negative semi-martingale convergence theorems,to obtain relaxed stability criteria and design controllers.These studies generalize the results of the current literature to a certain extent,and the main research contents are summarized as follows:1.For stochastic Markov jump systems with mixed time-varying delays and partly unknown transition rates,the exponential stability of the system in the mean square sense is studied by constructing a new stochastic Lyapunov functional.On the one hand,we derive sufficient conditions for guaranteeing mean square exponential stability of Markov jump systems,on the other hand,we derive sufficient conditions for uncertain Markov jump systems.Further,numerical simulation is presented to illustrate the effectiveness and less conservative of the proposed sufficient conditions for system stability;2.A class of stochastic neutral-type Markov jump systems with mixed timevarying delays is studied.An appropriate stochastic Lyapunov functional is constructed to analyze the stability problem of the system.When analyzing the system stability,we introduce some free weight matrices to deal with the derivative of the delay state.Furthermore,sufficient conditions are given to stabilize the stochastic neutral-type system.Finally,numerical simulation is used to verify the effectiveness of the proposed sufficient conditions for system stability;3.A class of neutral-type neural networks with Levy noise and mixed time-varying delays is studied.A new stochastic Lyapunov functional is proposed to solve the stability and stabilization problems of the system.On the one hand,we derive the corresponding sufficient conditions for guaranteeing mean square exponential stability,on the other hand,we propose the corresponding sufficient conditions of stabilization.Further,numerical simulation is used to verify the effectiveness of the proposed sufficient conditions for system stability;4.A class of stochastic neutral-type neural networks with Levy noise and sampleddata loss is discussed,and the synchronization problem of the system is studied.Firstly,an event-triggered control scheme is employed to overcome the occasional sampleddata loss problem.Secondly,we propose a new stochastic Lyapunov functional and give the sufficient conditions for guaranteeing almost sure stability of the corresponding synchronization error system.Finally,the numerical simulation is used to show the effectiveness and less conservative of the proposed results.