Research On Stability And Stabilization Of Several Classes Of Neutral-Type Stochastic Time-Delay Systems

Many practical engineering problems can be modeled by neutral-type time-delay systems.Since the derivatives contain difference operators,the analysis and design of neutral-type time-delay systems are more difficult than the general retarded-type time-delay systems.Neutral-type stochastic time-delay systems which combine the character-istics of both neutral-type time-delay systems and stochastic systems,can simulate some practical systems more accurately.It is therefore of great significance to study neutral-type stochastic time-delay systems in theory and engineering.The stability of difference operators is a necessary condition for the stability of neutral-type stochastic time-delay systems.However,the difference operators considered in the existing literature either have simple forms or are required to satisfy strict conditions.In view of this,the disserta-tion aims to relax the restrictive requirements for difference operators and study the stabil-ity and stabilization of neutral-type stochastic time-delay systems with complex difference operators.In addition,in the study of stability problems based on Lyapunov-Krasovskii functional（L-K functional）,the construction of L-K functional mostly depends on the ex-perience of researchers and lacks guiding principles,which leads to the derived stability conditions with complex forms and high conservatism.Therefore,this dissertation also focuses on exploring the systematic construction method of L-K functional.The main contents in this dissertation are summarized as follows:The stability of continuous difference equations describing difference operators is studied.In order to reduce the conservatism and complexity of stability conditions,a sys-tematic construction method of complete integral-type L-K functional is proposed.Based on the constructed L-K functional,sufficient conditions to ensure the L₂-exponential sta-bility and exponential stability of continuous difference equations are established.Then the exponential convergence rate is analyzed by introducing a suitable state transforma-tion.For the system with norm bounded parameter uncertainty,the sufficient conditions for stability are provided.The stability and stabilization of a class of linear neutral-type stochastic systems with two delays and Markov switching are studied.For wider application,an additional condition is proposed for the difference operator,which is less conservative and conducive to the stability analysis of the overall system.By constructing a novel L-K functional and using weighted norms,the analysis methods for mean square exponential stability and almost surely exponential stability are established.On the basis of stability analysis,a delay feedback controller based on difference operator is designed.The stabilization conditions in terms of linear matrix inequality are established by linearization methods,and the robust exponential stability and stabilization of the system in the presence of parameter uncertainty are discussed.The stabilization of a class of highly nonlinear neutral-type stochastic systems with multiple delays and Markov switching is studied.Since the studied system is highly non-linear,a new Khasminskii-type condition is proposed to replace the linear growth condi-tion.Combined with the conventional technique of stopping times,Gronwall inequality and Young inequality,the existence,uniqueness and boundedness of the global solution are proved.For the unstable system,a delay feedback controller is designed.In particu-lar,the conditions in terms of M-matrix for the control function are proposed,which are convenient for derivation and calculation.Using the method of Lyapunov functional,new asymptotic stabilization and exponential stabilization theories are established.In order to show the correctness and effectiveness of the theoretical results,numeri-cal examples are given to verify the above contents in the dissertation.