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The coarsest lattice that determines a discrete multidimensional system
Journal
Mathematics of Control, Signals, and Systems
ISSN
09324194
Date Issued
2022-06-01
Author(s)
Pal, Debasattam
Shankar, Shiva
Abstract
A discrete multidimensional system is the set of solutions to a system of linear partial difference equations defined on the lattice Zn. This paper shows that it is determined by a unique coarsest sublattice, in the sense that the solutions of the system on this sublattice determine the solutions on Zn; it is therefore the correct domain of definition of the discrete system. In turn, the defining sublattice is determined by a Galois group of symmetries that leave invariant the equations defining the system. These results find application in understanding properties of the system such as controllability and autonomy, and in its order reduction.
Volume
34
Publication link
Subjects