Algebraic results for linear-equation structures involving polynomial block-matrix partitions. Some implications in decentralized control theory.

*(English)*Zbl 0722.93013Summary: This paper outlines as first objective a set of previous results in the field of algebraic systems theory for the case of block-partitioned polynomial matrices. The formulation is relevant for obtaining a mathematical outline being available for analysis of fixed modes when transforming a decentralized information, which involves the use of local controllers of which each one uses a part of the output components for feedback, in the centralized one. This centralized controller involves the use of a controller which possesses all the information, being available by feedback. The main theoretical results are presented in the ring of polynomial matrices and the associated ring of quotients of rational matrices. The results are extendable without difficulty to other sets of matrices over rings.

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\textit{M. de la Sen}, Math. Comput. Modelling 15, No. 1, 47--63 (1991; Zbl 0722.93013)

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