A general realization theory for higher-order linear differential equations

Abstract

In this note we show that the geometric quotient, under a natural group action, of the generalized state space systems recently considered by Schumacher, Kuijper and Geerts is algebraically isomorphic to the space of a homogeneous autoregressive system. This result essentially follows from work of Stromme published earlier in the algebraic geometry literature. In particular, these generalized state space systems represent a realization of the space of homogeneous autoregressive systems.