(A,B)-cyclic submodules Original Research Article

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.