Abstract
An ( A, B)-cyclic submodule M is generated by the states of one single trajectory of a linear control system whose parameters come from a commutative ring. M is “finite”, when it is generated by the states of a “deadbeat-control” process. Motivations and basic properties of such modules are given and among several further results it is shown that the family of finite ( A, B)-cyclic submodules is an invariant which (e.g., over polynomials) can be determined by an appropriate Gröbner basis computation.
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