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On feedback invariance properties for systems over a principal ideal domain

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3 Author(s)
Assan, J. ; Inst. de Recherche en Cybernetique de Nantes, France ; Lafay, J.F. ; Perdon, A.M.

Simple necessary and sufficient conditions for the solvability of many control problems for linear systems over a field are based on the equivalence between the (A, B)-invariance property and the (A+BF)-invariance, or feedback invariance, property. For systems over a ring, this equivalence is no longer true and many results of the geometric control theory cannot be extended. We present new, algorithmically checkable characterizations of the (A+BF)-invariance property for systems defined over a principal ideal domain and a new solvability condition for the disturbance rejection problem

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Automatic Control, IEEE Transactions on  (Volume:44 ,  Issue: 8 )