H_∞Filter Design For Several Classes Of Time-delay And Saturation Systems With Applications

The H∞filter problem is of both theoretical and practical importance in control design and signal processing, and has received wide attentions and researches. It is concerned with the design of dynamic systems guaranteeing the robustness against uncertain parameters and external noises, and makes no assumptions on the priori knowledge of the external noisies or precise mathematical models except for the only bounded energy. All these make the H∞filter has important application in practical engineering. However, practical filter systems are inherently subject to many non-linear effects which may restrict the operation, result in instability, deteriorate the performance indicators and even cause serious consequences. Saturation and time delay are two prominent factors and have received wide attentions. However, to our best knowledge, the existing results on the design of H∞filter for linear systems are either with time delay or with saturation. Moreover, there are fewer results for the nonlinear systems.This paper investigates the H∞filter design problem for several classes of time-delay and saturation systems and its applications. The main contents of this thesis are composed of the following parts:1. The design of robust H∞filter for a class of time-delay linear systems with saturation is investigated. A linear filter structure is given, and a new design method is proposed. Using the Lyapunov-Krasovskii stability theory and LMIs, we give some sufficient conditions for the existence of a feasible solution to the problem, which guarantee that the filtering error system is asymptotically stable and satisfy the H∞performance constraint for all admissible disturbances. In addition, we also establish a LMIs approach to the robust H∞filter design. Two practical examples as well as the comparison with the existing results verify the validity and superiority of this method. 2. The design of the robust H∞filter for the Hamiltonian systems with time delay or with saturation is studied. Based on the structure of Hamiltonian systems, we first propose a nonlinear filter structure. Then, considering the influence of time delay and saturation, we present methods for the filter design. Methods to handle time delay and saturation are given, respectively. Finally, simulation examples are studied to prove the validity of this method.3. The stability analysis and H∞filter design for general nonlinear systems are considered, which are based on Hamiltonian structure and T-S fuzzy control. First, the nonlinear system is fuzzified into several fuzzy Hamiltonian subsystems. Then, its stability is analyzed, and a fuzzy H∞filter design method is given. Finally, a simulation example prove the validity of this method.4. The design of robust H∞controller and filter for nonlinear Hamiltonian network systems is discussed. Based on reasonable assumptions and processing methods, we convert the uncertainty network time delay and packet loss into time-varying delay. Then, we obtain the design methods of the H∞controller and filter. Finally, examples on circuit systems testifies the validity of the method.