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Minimality and observability of group systems. (English) Zbl 0813.93046

Authors’ summary: Group systems are a generalization of Willems-type linear systems that are useful in error control coding. It is shown that the basic ideas of Willems’ treatment of linear systems are easily generalized to linear systems over arbitrary rings and to group systems. The interplay between systems (behaviors) and trellises (evolution laws) is discussed with respect to completeness, minimality, controllability, and observability. It is pointed out that, for trellises of group systems and Willems-type linear systems, minimality is essentially the same as observability. The development is universal-algebraic in nature and holds unconditionally for linear systems over the real numbers.

MSC:

93C25 Control/observation systems in abstract spaces
93B20 Minimal systems representations
93B07 Observability
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References:

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