Analysis And Design For Stochastic Nonlinear Systems With Time-delay

Ever since the stochastic stability theory is established and improved,the feedback controller design and stability analysis for stochastic nonlinear systems have received various theoretical results.As we all know,time-delay phenomenon exists in various engineering systems such as engineering technology,social economy,the ecological environment and so on.And the existence of time-delay is an important source of instability and poor performance.Therefore,no matter in theory or in engineering practice,the control design of stochastic nonlinear time-delay systems has been received much attention.In this paper,based on the Razumikhin-Mao theory on stochastic systems and Back-stepping design technique.An adaptive state feedback controller and output feedback controller are constructed to render the closed-loop system globally asymptotically stable in probability.The main contributions include:1.The Razumikhin-type approach is introduced to solve the state feedback stabilization problem for a class of stochastic high-order nonlinear systems with time-varying delay in this paper.Based on the general Razumikhin-type theorem on stochastic systems established and Back-stepping design method,a state feedback controller is constructed to ensure the origin of closed-loop system is globally asymptotically stable in probability.Our methodology enables us to completely remove the limitations on the derivative of delay,which is the common assumption of stochastic high-order nonlinear systems with time-varying delay.The efficiency of the state feedback controller is demonstrated by simulation example.2.In this chapter,we consider the problem of output feedback stabilization for a class of stochastic high-order nonlinear systems with time-varying delay in order to reduce the impact of the condition that not all of the state vectors are measurable.Based on the stochastic nonlinear systems' stability theories,by combining with the Back-stepping design technique and choosing an appropriate Lyapunov-Krasoviskii functional,adaptive state feedback controllers and output feedback controllers are constructed for the systems.An output feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability.A simulation example showed the effectiveness of the designed controller.3.In this chapter,we extend the study by extending the stable feedback controllers for objects to a class of stochastic nonlinear systems with time-varying delay.By choosing proper Lyapunov-Krasovskii function,based on the Razumikin-Mao theory stochastic systems and Back-stepping design technique,by using the technique of inequality,the problem of memory state-feedback controller is investigated.A memory state-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability.The effectiveness of the designed controller is demonstrated by a simulation example.