This paper introduces the concept of a controllability module and then uses it to study certain algebraic properties of index-invariant, time-varying, linear systems. It is shown that controllability modules possess a property similar to the pole placement property of controllability subspaces. Application of controllability modules to index-invariant systems leads to a new construction of Brunovský’s decomposition which serves to clarify the algebraic relationships upon which the decomposition is based.
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Morse et al. (1973) studied this question.
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