Algebraic characterization of autonomy and controllability of behaviours of spatially invariant systems

TL;DR

This paper provides algebraic criteria to determine autonomy and controllability of spatially invariant dynamical systems described by PDEs with periodic solutions, using polynomial matrix representations.

Contribution

It introduces algebraic characterizations for autonomy and controllability of behaviors in spatially invariant systems with periodic solutions, advancing theoretical understanding.

Findings

Algebraic criteria for autonomy established

Conditions for controllability derived

Applicable to systems described by polynomial matrices

Abstract

We give algebraic characterizations of the properties of autonomy and of controllability of behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system pf partial differential equations corresponding to a polynomial matrix M in (C[\xi_1,...,\xi_d, \tau])^{m \times n}.