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On feedback invariance properties for systems over a principal ideal domain

On feedback invariance properties for systems over a principal ideal domain,10.1109/9.780439,IEEE Transactions on Automatic Control,J. Assan,J. F. Laf

On feedback invariance properties for systems over a principal ideal domain   (Citations: 5)
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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
Journal: IEEE Transactions on Automatic Control - IEEE TRANS AUTOMAT CONTR , vol. 44, no. 8, pp. 1624-1628, 1999
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    • ...The same kind of generalization, which was initiated by Hautus, Conte and Perdon, has been widely studied for linear dynamical systems over rings (see [Hau82, Hau84, CP94, CP95, Ass99, ALP99])...
    • ...In the case of the theory of linear dynamical systems over a field, the sequence {Xr}r∈N always converges in at most n steps, since it is a decreasing sequence of subspaces of a vector space of dimension n. However, one of the problems in the max-plus case, which is reminiscent of difficulties of the theory of linear dynamical systems over rings (see [Ass99, ALP99, CP94, CP95, Hau82, Hau84]), is that the sequence {Xr}r∈N may not stabilize ...
    • ...Once again, this problem is reminiscent of difficulties of the theory of linear dynamical systems over rings (see [Hau82, Hau84, CP94, CP95, Ass99, ALP99])...

    Ricardo David Katz. Max-Plus (A,B)Invariant Spaces and Control of Timed Discrete-Event Sys...

    • ...has been satisfactorily solved (see [3], [2], [1])...
    • ...Further results along this line, obtained relaxing conditi on (22), are contained in [1]...

    G. Conteet al. Modeling Time-delay Systems by means of Systems with Coefficients in a...

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