ABSTRACT
Model reduction of dynamical systems has its roots in many different fields of applied mathematics. The earlier occurrence of such techniques is the approx imation of rational functions of high degree by one of lower degree. The first results in that area were formulated in a m athem atical setting and included techniques such as Padé approximations, continued fraction expansions and so on [3]. Such results were also used in the context of model reduction techniques or approximation techniques in application areas such as signals and systems, and lead to the synthesis of approximating systems by one of a prespecified degree. Examples of algorithmic developments in this area are the Remez al gorithm in filter design and the Massey Berlekamp algorithm in convolutional codes. More recent developments in linear systems theory are nicely synthesized
in But these developments are referring mainly to the area of linear timeinvariant dynamical systems. In this chapter we have tried to establish connec tions between different projection techniques used in the area of systems and control and in particular showed how to extend this to the time-varying case. We also tried to show the connection with a popular technique for nonlinear dynamical systems.
