Computation of maximal pre-controllability submodules over a Noetherian ring

Abstract

For dynamical systems with coefficient in a ring it is not always possible to compute by a finite procedure the maximal ( A, B)-invariant submodule contained in the kernel of the output map C, namely V ∗( Ker C) . This difficulty prevents one from checking necessary and sufficient geometric conditions for the solvability of noninteracting control problems. In this paper we will prove that, for dynamical systems with coefficients in a Noetherian ring, it is always possible to compute by a finite procedure the maximal pre-controllability submodule contained in the kernel of the output map C, namely R ∗( Ker C) . This result is useful in dealing with the block decoupling problem or the disturbance rejection problem.