Title :
Recurrence and finiteness for systems in a general setting
Author :
Arbib, M. ; Manes, E.G.
Author_Institution :
University of Massachusetts at Amherst, Amherst, Massachusetts
Abstract :
An X-system is G : I ?? Q, Fx : Q ?? Q (x ?? X) and H : Q ?? Y. X-systems generalize linear and bilinear systems over a ring. If I and Y are finite, morphic recurrence is necessary and sufficient for a finite realization. For systems over a ring, if X is finite and if Y is an Artinian, injective module, morphic recurrence is necessary and sufficient for an Artinian realization. For systems with equationally-definable state space, a Hankel matrix has finite rank if and only if it has an Artinian, Noetherian realization.
Keywords :
Equations; Information science; Linear systems; Mathematics; Modules (abstract algebra); Nonlinear systems; Polynomials; Roentgenium; State-space methods;
Conference_Titel :
Decision and Control including the 15th Symposium on Adaptive Processes, 1976 IEEE Conference on
Conference_Location :
Clearwater, FL, USA
DOI :
10.1109/CDC.1976.267665
