Many Researches On Robust Filtering Problem

State filtering has been attracting much attention as one of important fields in controltheory and engineering application. In many practical applications, however, the statisticalproperties of exogenous noise signals are rarely known and there are perturbations insystem model, that is, exogenous disturbances and uncertainties in system model, so therehas been rapidly growing interests in robust filtering. In the past decades, robust filteringwas studied and amount of meaningful results were obtained, but, the delay-dependentrobust filtering for time-delay systems and robust filtering for nonlinear systems have notbeen fully investigated.The main content of this thesis can be briefly described as follows:The history and research status of robust filtering are introduced systematically, theemphasis is focused on the representative algorithms and results in the development ofrobust filtering theory and we forecast the problem and development in the future.We developed a robust filtering algorithm for a class of time-varying delayuncertainty linear systems, a new Lyapunov-Krasoviskii functional is given andbounded-real lemma is used in order to design a delay-dependent H_∞filter.The Riccati equation method is used for uncertain neutral delay system, the suitablefilter can be obtained by solving a pair of Riccati equation, the cycle of solving andjudging is omitted. Considering the convenient and effective algorithm of LMI, we use itas a design tool. A sufficient condition for the existence of H_∞filter is given andformulated in terms of linear matrix inequalities.The study of neutral delay systems with distributed delays is not sufficient, so it is stillessential to study this system. Some over-bounding techniques of inequality were proposedthat reduces the conservativeness coming from the derivative of Lyapunov function. Thenorm bounded uncertainty in system is regarded as exogenous disturbance, so theconservativeness is degraded in the proof of BRL and better H_∞index is obtained, what'more, the filtering problem is solved when there are distributed delays in measurementequation. An approach introduces a slow-type state transformation and is based onrepresenting the augmented system by a descriptor system and designing a H_∞filterwhich guarantees the performance level for the descriptor model. The numerical exampleis provided to demonstrate the effectiveness of the proposed method.The other important content is about robust filtering for nonlinear system. T-S fuzzy model is used to describe kinds of nonlinear systems. The delay-dependent H_∞filter forcontinuous time delay T-S fuzzy model and discrete time delay uncertainty T-S fuzzymodel are studied respectively, the sufficient condition is given, and the method isdeveloped by considering time delays. We studied robust H_∞filtering for a descriptornonlinear time-delay system based on T-S fuzzy model. The fuzzy filter can insure theerror filtering system is regular, impulse-free and asymptotically stable.