Chapter 16 Linear Time-Variant Systems Sự phức tạp của các hiện tượng vật lý nghiên cứu không có thể được giảm xuống chỉ có một mô hình hệ thống tuyến tính năng động với hệ số không đổi. Những mô hình này đôi khi kém thích nghi, ví dụ, họ chỉ có thể đối phó với cường độ có một mối tương quan giảm theo cấp số nhân. Tuy nhiên, trong các lĩnh vực đầy đủ giống như thủy văn [Hur 65], điện tử [Văn 88], giao thông [Rie 97, WIL 95, kỹ thuật điện [CHA 81] và cơ khí [CLE 98,. | Chapter 16 Linear Time-Variant Systems The complexity of the physical phenomena studied cannot be reduced to only one modeling by linear dynamic systems with constant coefficients. These models are sometimes poorly adapted because for example they can only deal with magnitudes having an exponentially decreasing correlation. However in fields full of variety such as hydrology HUR 65 electronics VAN 88 traffic RIE 97 WIL 95 electrical engineering CHA 81 and mechanics CLE 98 ZHU 96 there are many situations that generate behaviors that do not obey these quite simple models. Therefore in the last 30 years new analysis models and tools have appeared. In this perspective one of the goals of research is to extend the class of linear dynamic systems by including those for which the coefficients vary in time. These variations can be divided into two classes. The first class concerns the sudden non-stationarities or failures characterized by time intervals where the coefficients are constant. The non-stationarity is due only to the presence of instantaneous shifts in their values. This modeling is found for example in the field of monitoring and diagnostic BAS 93 . As such the problem is to essentially detect the instants of change as well as the amplitude of the parametric shifts. The second class pertains to the systems where the coefficients are functions of time. When these dynamics are slow with respect to those of the system they can be dealt with through adaptive techniques. However there are also many cases in which the evolution of parameters is fast T-periodic systems RAB 92 auto-similar systems GUG 01 etc. . This last category makes the development and the implementation of specific methods in Chapter written by Michel GUGLIELMI. 522 Analysis and Control of linear Systems both the control and identification fields indispensable. Firstly it is important to have the basic mathematical tools indispensable to their analysis. This chapter is dedicated to the analysis .
