H_? Control And Filter For A Class Of Nonlinear Stochastic Systems Driven By Both Poisson Jump And Brownian Motion

Many practical systems are often subject to the parameter perturbation,external noise and time-delay,which often lead to system performance degradation or even instability.How to deal with these factors and maintain good robustness of the considered systems have always been a concern of researchers.In order to better study the influence of external noise on the system performance,the stochastic differential equation is introduced to model such systems in which the Brownian motion is used to describe the external noise.On the other hand,many unpredictable emergencies,such as sudden faults and sudden changes in critical values of system parameters of the considered systems,are often encountered in the process of the system operation,and the Poisson process can well describe this jump stochastic phenomena.Therefore,the study of stochastic time-delay systems with the Poisson jump and Brownian motion has both theoretical significance and practical application value.This thesis mainly studies the H? control and filtering of this class of system.Based on Lyapunov stability theory,this thesis studies the H? control and filtering of nonlinear stochastic systems with continuous Brownian motion and discontinuous Poisson process by using Ito formula,stochastic analysis principles and completing the square.Firstly,the H? control problem of a class of nonlinear stochastic systems with Poisson jump is discussed by means of generalized Ito formula and completing the square.Secondly,in order to estimate the internal state of the considered system,the exponential mean square H? filtering and asymptotic mean square H? filtering are studied by using the nonlinear stochastic bounded real lemma.Finally,for a class of nonlinear stochastic time-delay systems with Poisson jump,the H? control and filtering problems are discussed.According to the conclusions obtained in this thesis,some numerical examples are given to illustrate the effectiveness of the obtained results.