A New Approach to the Theory of Canonical Decomposition of Linear Dynamical Systems

Abstract

In this paper, a new approach to the structure theory of linear dynamical systems is developed. Based on the structural properties of influenceability and invisibility and without introducing any limiting hypotheses, the existence of a canonical decomposition of the state space into subspaces of constant dimensions is proved. Furthermore, the existence of the canonical form of the equations, and also the uniqueness of this form within an equivalence class are proved, the latter also being determined. The general structure theory obtained in this way comprises all the hitherto known results and in particular yields a constant decomposition for time-invariant systems.