Overview

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 nonstationarities 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...