Robust Filter Design For Uncertain Stochastic Systems

Filtering problem has long been one of important fields in control and signal processing. Since the optimal filtering theory of stochastic system was proposed, the theory of Kalman filtering for stochastic systems is widely used in fields of telecommunications, aerospace, aviation, industrial process control and so on, but Kalman filtering requires that system model under consideration is accurately known and the external interference signals are with known statistical properties. However, in many actual systems, the exact system model or the statistical properties of the unknown external disturbances is difficult to obtain, or the system may drift, all of which may result in uncertainties. In such cases, research on improving the filtering algorithms, such as robust H∞, robust L2-L∞filtering, is of great significance.Stochastic system is a class of systems that widely used in practice, which contains a series of stochastic variables, such as internal stochastic parameters, external stochastic disturbances and observation noise. These stochastic variables can not be described by known function of time, we can only understand some of its statistical properties, and also the system states can not be determined by observation. In practice, in many cases many stochastic factors of the system can not be ignored, so study on the filtering design problem for uncertain stochastic system is of great significance.In this thesis, we will investigate the robust filter design problems for several classes of nonlinear uncertain stochastic systems, the main work are generalized as follows.1) The robust L2-L∞filtering problem for a class of nonlinear uncertain stochastic delay systems-stochastic fuzzy delay systems is investigated. Attention is focused on the design of a fuzzy-rule-dependent filter that ensuring both the robust stability and a prescribed L2- L∞performance level of the filtering error system. An approach called weighting-dependent is adopted and delay-dependent sufficient conditions for the solvability of the problem are presented based on the linear matrix inequalities (LMIs) approach.2) The problem of robust L2-L∞filtering for a class of nonlinear uncertain stochastic systems is addressed. The nonlinear uncertainties in the model are vector-bounded as an extension to the usual Lipschitz conditions, which makes the model more representative and practical. By proposing a stochastic integral inequality, we designed a stochastic L2-L∞filter that ensuring both the asymptotic mean-square stability and a prescribed L2-L∞performance level of the filtering error system. Sufficient conditions which can guarantee the existence of the desired filter are also obtained by using the Lyapunov stability theory.3) The robust passive filtering for a class of uncertain stochastic neutral systems with nonlinear perturbations is investigated. The system under consideration contain time varying but norm bounded parameter uncertainties, stochastic disturbance, time-varying delay and vector-bounded nonlinearities. By combining ltd's differential rule with the stochastic Lyapunov stability theory, we design a full-order filter such that the dynamics of the filtering error system are guaranteed to be regular, robustly asymptotically stable in the mean square for all admissible uncertainties and nonlinearities, and the proposed passive performance is satisfied.