Discrete Systems With Infinite Distributed Delay H_ ¡Þ Filter Design

In industrial systems the time-delay phenomenon is very common, such as long pipe feed, belt transmission, miracle slowly process, complex on-line analyzers and so on. In addition, for many time constant systems, also used proper time constant delay link to approximate. The model is summarized as time-delay systems. Generally, the reason of the time-delay is that the original materials and the information transmission are caused in the systems. Therefore, we can find many typical systems in our life, for example, the communication systems, the transmission systems, the chemical process system, the metallurgical process system, the environmental system, the power system and so on.It is complex and difficult to analysis and comprehensive the time-delay phenomenon in the systems. The existing of the time-delay is the root of unstable and performance deteriorated in the systems. Because of this reason, it is a hot issue in the control theory and control engineering field. Based on the Lyapunov approach and the LMI, we can get the methods and results about the analysis and comprehensive in the robust systems. The filter has a wide application in the radar design, the fault detection, and the signal processing and so on. For an accurate system, we can estimate the error to measure the performance index. Further, we can use it to design the filter system. We can also use a transfer function as a performance index when the characteristic of the disturbance is not sure. This paper mainly consists of 4 chapters.Chapter 1 the research background and significance are introduced, and the phylogeny of this whole field and the main results in existence are summarized respectively. The preparative knowledge is also presented roundly.Chapter 2 considers a system with the infinitely distributed delay. First we research the sta-bility of the systems, second we design stable H∞filtering. This filter can guarantee that the whole systems signals asymptotically track the desired signals. A simulation example further demonstrates the efficiency of the control scheme.Chapter 3 considers a many cell type of uncertain time-delay systems. The parameters are assumed to be unknown but belonging to known convex compact of polytope type, our aim is to design stable H∞filtering. This filter can guarantee that the whole systems signals asympotot- ically track the desired signals. A simulation example further demonstrates the efficiency of the control scheme.Chapter 4 summarizes the main results of this paper and a prospect of the future research work.