Research On Non-fragile Filtering Methods For Several Kinds Of Systems

With the gradual maturity of H∞ filtering theory, combining with considering the uncertain factors existing in the practical process of filter realization, more and more attention has been paid to the research of non-fragile H∞ filtering algorithm. Different from the traditional point to point control system, networked control systems have brought many advantages. However, the introduction of the network has also brought problems, such as delays, missing measurements, nonlinearities, channel fadings, etc., and this has given the analysis and design of the networked control systems a more practical significance, as well as difficulties. In this paper, by the Lyapunov stability theory, LMI technology and stochastic analysis technology are utilized to model the complicated networked control systems, and the design method of non-fragile H∞filter is probed. The contributions of this paper are as follows:Firstly, the research methods of H∞ filters for several kinds of systems with multiplicative and additive gain uncertainties are discussed, respectively. By the LMI approach, the sufficient condition of the non-fragile filters is obtained, which ensures the estimation error augmented system asymptotically stable and the H∞ index from the external signal to the estimation error be under a given level, and the research results are analyzed.Secondly, a L-th Rice fading model is established for the discrete system considering fading channels, and a kind of fixed non-fragile filter is designed. After defining the filtering error system and the H∞ performance index, the Lyapunov functions are selected. According to the Lyapunov stability theory, stochastic analysis method and Kronecker product, the mathematical expectations of the differential of functions are calculated. Then the cost function is acquired referring to the H∞ performance index. By the calculation based on LMIs, the sufficient condition which satisfies the asymptotic stability of the filtering error augmented system and H∞ performance restraint is obtained, as well as the gains of the filter. YALMIP toolbox of the MATLAB software is utilized to figure out the feasible solution of the standard LMI problem, and the effectiveness of the algorithm is verified through the simulation.Thirdly, the non-fragile H∞ filtering method for discrete time-delay systems with random package dropouts is studied. The random variables that conform to Bernoulli distribution are adopted to represent the phenomenon of randomly occurred missing measurements in the network. Infinite-distributed delays models are used to depict the phenomenon of time delay. And the target is to investigate a filter with randomly occurring gain variations, with the random variables being Gaussian type. The design method of non-fragile H∞filter for the discrete system with fading channels is employed to this kind of system, the sufficient condition of the existence of the desired filter, and the feasibility of the design are validated.Finally, the non-fragile H∞ filtering algorithm for nonlinear system with channel fadings is researched. The nonlinear phenomenon is reflected by the Bernoulli typed random variables and the sector bounded condition, combining with the model of channel fadings, the non-fragile H∞ filter with randomly occurring gain fluctuations is designed. Expand the design idea of non-fragile filter for discrete system with fading channels to this comprehensive system, through its process of stochastic analysis, the LMI which needs to be satisfied to realize the desired filter is acquired. That is to say, the non-fragile filter design is converted into a convex optimization problem which can be solved by the semi-definite programmable method, and the accuracy of the research is illustrated by the simulation example.