Behavior decompositions and two-sided diophantine equations

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.