Elements of Linear System Theory

Abstract

This chapter is devoted to a short introduction to algebraic system theory. We shall focus on the main conceptual underpinnings of the theory, more specifically on the themes of external and internal representations of systems and the associated realization theory. We feel that these topics are to be considered an essential part of linear algebra. In fact, the notions of reachability and observability, introduced by Kalman, fill a gap that the notion of cyclicity left open. Also, they have such a strong intuitive appeal that it would be rather perverse not to use them and search instead for sterile, but “pure,” substitute terms.