Matricial decomposition of systems over rings

Abstract

Abstract. This paper extends to non-controllable linear systems over rings the property FC s (s > 0), which means "feedback cyclization with s inputs": given a controllable system (A, B), there exist a matrix K and a matrix U with s columns such that (A + BK, BU ) is controllable. Clearly, FC 1 is the usual FC property. The main technique used in this work is the obtention of block decompositions for systems, with controllable subsystems of a certain size. Each of the studied decompositions is associated to a class of commutative rings for which all systems can be decomposed accordingly. Finally, examples are shown of FC s rings (for s > 1) which are not FC rings.

Feedback Classification of linear systems and convolutional codes. Applications in cybernetics, coding theory and cryptography = Feedback clasificación de sistemas y códigos de convolución. Aplicaciones en cibernética, teoría de códigos y criptografía

“…La clase de anillos von Neumann regulares han sido estudiados desde el marco de sistemas lineales de control, veáse [16], [72], [73], [74] y [75]. El primer ejemplo de anillo conmutativo von Neumann regular es Z/lZ con l = p 1 .…”