H_? Filtering For Some Classes Of Stochastic Nonlinear Systems With Applications

There has been increasing research interest in H? filtering problem due to its im-portant theoretical and practical significance in control design and signal processing.The H? filtering is a kind of robust filtering method which combines the robust control with the filtering theory.It is not necessary to exactly know the statistical properties of the ex-ternal disturbance which is assumed to have bounded energy.At the same time,with the growing complexity of dynamic systems,the stochastic nonlinear systems have attracted considerable attention and have become a popular research field.In recent years,many scholars have done a lot of important researches for H? filtering problem,and there have been many meaningful results.However the H? filtering problem for stochastic nonlinear systems has not been fully investigated.This dissertation considers the H? filtering problem for some classes of stochastic nonlinear systems with applications,and the main research results of this dissertation are summarized as follows:(1)The H? filtering problem for a class of stochastic nonlinear systems with time-delay is studied.By a sufficient condition of stochastic input-to-state stability,linear matrix inequality(LMI)and Jensen inequality,a sufficient condition is given to ensure both stochastic input-to-state stability and a prescribed H? attenuation level for the cor-responding filtering error system.When the LMI is feasible,an explicit expression of a desired filter is presented.A practical example is employed to illustrate the effectiveness of the proposed approaches.(2)The H? filtering problem for piecewise homogeneous Markovian jump nonlinear systems is investigated.Different from the existing studies in the literatures,the existence of variations in transition rates for Markovian jump nonlinear systems are considered.The mode-dependent and mode-independent filters are designed such that the dynamics of the filtering errors are stochastic integral input-to-state stable with H? attenuation level.Using the Lyapunov functional method and LMI method,sufficient conditions for the solution to the H? filtering problem are derived.The practical example is proposed to illustrate the effectiveness of the given theoretical results.(3)The finite-time stochastic input-to-state stability for stochastic nonlinear systems and the H? filtering problem for a class of stochastic nonlinear singular systems are investigated.The nonlinear term of the stochastic nonlinear system does not satisfy the Lipschitz condition.First,a sufficient condition of finite-time stochastic input-to-state stability for stochastic nonlinear systems is proposed.Secondly,based on the sufficient condition,a normal filter is designed.Finally,sufficient conditions for the solution to the H? filtering problem are derived.(4)The H? filtering problem for stochastic fuzzy singular systems with time-varying delay is investigated.A fuzzy filter is designed to estimate the unmeasured state variables.Based on an auxiliary vector and an integral inequality,the delay-dependent sufficient conditions are established,which ensure that the filtering error system is e?t-weighted integral input-to-state stable in mean.The sufficient conditions for the solvability of the H? filtering problem are obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities.(5)The H? filtering problem for a class of biological systems is studied.Singular system theory is utilised to build a stochastic singular food chain system.The full-order and reduced-order filter are designed to estimate the unmeasurable state variables of the food chain system.The definition of L2—gain?? is given to ensure the solvability of the H? filtering problem.By Ito formula,implicit function theorem,Lipschitz condition and linear growth condition,a sufficient condition of L2-gain ?? for food chain system is obtained.