Behavior decompositions and two-sided diophantine equations

Citation
M. Bisiacco et Me. Valcher, Behavior decompositions and two-sided diophantine equations, AUTOMATICA, 37(9), 2001, pp. 1387-1395
Citations number
10
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
AUTOMATICA
ISSN journal
00051098 → ACNP
Volume
37
Issue
9
Year of publication
2001
Pages
1387 - 1395
Database
ISI
SICI code
0005-1098(200109)37:9<1387:BDATDE>2.0.ZU;2-E
Abstract
In this paper, the relationship between the decomposition of (linear, time- invariant, differential) behaviors and the solvability of certain two-sided diophantine equations is explored. The possibility of expressing a behavio r as the sum of two sub-behaviors, endowed with a finite dimensional (and h ence autonomous) intersection, one of which is a priori chosen, proves to b e related to the solvability of a particular two-sided diophantine equation . In particular, the existence of a direct sum decomposition is equivalent to the solvability of a two-sided Bezout equation, and hence to the interna l skew-primeness of a suitable matrix pair. (C) 2001 Elsevier Science Ltd. All rights reserved.