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Matricial decomposition of systems over rings. (English) Zbl 1170.93010
Summary: 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.
MSC:
93B05 Controllability
93C05 Linear systems in control theory
93B25 Algebraic methods
93B55 Pole and zero placement problems
13C99 Theory of modules and ideals in commutative rings
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