Uncertain Discrete Systems H_ ¡Þ Non-fragile Filter Design

In recent years, the problem of robust control and filter are researched by many scholars. But in fact, we find that the factors about the limitations of computer word length and the factors of aging components.It may cause filtering parameters to have small variation. This will make the filtering performance reduce or even disappear completely. So the filter exist imprecision and uncertain factor. Thus, the non-fragile filtering question is concerned by many scholars.The thesis considers the non-fragile H_∞filtering problem for uncertain discrete-time systems. We give sufficient conditions for solving problem and design the non-fragile filtering methods by adding the slack matrix and using LMI method. The main results are listed as follows:1. This chapter deals with the non-fragile H_∞filtering problem for uncertain discrete-time systems. It gives sufficient conditions for solving problem by adding the slack matrix and using LMI method in the existing methods. The non-fragile H_∞filtering problem can be based on a set of linear matrix inequalities (LMI) solution to design. This chapter increases the free dimensions of linear matrix inequalities solution by adding the slack matrix. By comparing the present results, it greatly reduces the conservativeness by adding slack matrix. A numerical example is given to illustrate the effect of non-fragile H_∞filtering problem.2. Based on these conclusions, we discuss the non-fragile H_∞filtering problem for polytypic uncertain discrete-time systems. We also give the conclusion of no adding the slack matrix. By comparing the present results, we show that adding slack matrix can reduce the design conservativeness3. We modify the error of this paper "Parameter-dependent robust H_∞filtering for uncertain discrete-time systems " which published in Automatica,2009. This paper exists an error in the proof of theorem. It leads to appear the error of the main results. An example is given to illustrate the wrong conclusions and shows our correctness of modifying conclusion.