REALIZATION OF CONTINUOUS-TIME LINEAR DYNAMICAL SYSTEMS: RIGOROUS THEORY IN THE STYLE OF SCHWARTZ

Abstract

This chapter discusses the realization of continuous time linear dynamical systems. The problem of realization has become well-established in system theory during the past decade. It concerns the question of replacing the external description of a dynamical by an internal description, using rigorous and mathematically natural constructions. The concept of realization is of major interest to differential equationists because it provides new reasons for studying important classes of differential equations as well as new viewpoints for attacking some of the classical problems. One emphasize right away that dynamical systems are understood here in the modern sense: The input/output behavior of the system receives equal attention with the internal behavior. The classical mathematical theory of dynamical systems deals exclusively with the latter; this point of view is extremely restrictive for the modern applications.