H_∞ Filtering Of 2-D Discrete System Based On Roesser Model

In order to solve the problems of various kinds of uncertainty in the system, the H∞ filter of two-dimensional discrete system apply the performance index of H∞ norm which introduced in the design of robust control to filter. Because the system exist process noise and measurement noise, perhaps there is parameter uncertainty in system, designing stable and less conservative filter is particularly important.The robust control theory is a powerful tool to deal with uncertainty problems. H∞ control theory is solving the problem of robust control relatively complete theoretical system.Control and filtering are the dual problems. In the same way, the H∞ filtering problem is developed based on the standard H∞ control problem. The H∞ filtering problem is a special H∞ control problem. Two-dimensional discrete system model has Attasi model, FM model and Roesser model ect. In this thesis it mainly study H∞ filtering problem of two-dimensional discrete system based on the Roesser model.The purpose is to design two forms of H∞ filter which can make any energy bounded noise input reduced to a certain level.First of all, in this thesis, it introduce the establishing process of Roesser model and some theoretical knowledge relevant in detail and provide a sufficient condition to filtering. Secondly, this thesis thoroughly discusses the H∞ filtering effect of discrete system and designs filter which can ensure the noise attenuation performance. Study the observer-based H∞ filter and the general form of H∞ filter respectively. Design observer-based H∞ filter by two options, linear matrix inequality method and riccati inequation method. The principle of these two options almost the same, but the linear matrix inequality approach is more superior to riccati inequality approach on the computing power. For the general form of H∞ filter, two theorems of linear matrix inequality approach are used to design.In MATLAB simulation environment, we verify these two types of filters through related image processing example. The general form of H∞ filter’s filtering effect is obviously better than the observer-based H∞ filter. The general form of H∞ filter has a good noise attenuation level.Application in the thermal engineering example, further verify the effect of the two forms of H∞ filters, which provides a new method to solve the problem of practical application.