Controlled invariance in systems over rings

M.L.J. Hautus

doi:10.1007/BFb0006823

Controlled invariance in systems over rings

M.L.J. Hautus

Center for Analysis, Scientific Computing and Applications

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

31 Citations (Scopus)

Abstract

The definition of controlled invariant (i.e. (A,B)-invariant) subspaces of a linear system is extended to systems over rings. It is observed that in this more general setting, the equivalence of the geometric and the feedback characterization is no longer true. Particular attention is paid to the weakly unobservable space V*, and conditions are given for this space to satisfy the feedback characterization. These conditions have the form of the existence of a factorization of the transfer function. An application to the disturbance rejection problem is given.

Original language	English
Title of host publication	Feedback Control of Linear and Nonlinear Systems (Proceedings of the Joint Workshop, Bielefeld, Germany, June 22-26, 1981 & Rome, Italy, June 29-July 3, 1981)
Editors	D. Hinrichsen, A. Isidori
Place of Publication	Berlin
Publisher	Springer
Pages	107-122
Number of pages	16
ISBN (Electronic)	978-3-540-39479-2
ISBN (Print)	3-540-11749-0, 978-3-540-11749-0
DOIs	https://doi.org/10.1007/BFb0006823
Publication status	Published - 1982

Publication series

Name	Lecture Notes in Control and Information Sciences
Volume	39
ISSN (Print)	0170-8643

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10.1007/BFb0006823

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Hautus, M. L. J. (1982). Controlled invariance in systems over rings. In D. Hinrichsen, & A. Isidori (Eds.), Feedback Control of Linear and Nonlinear Systems (Proceedings of the Joint Workshop, Bielefeld, Germany, June 22-26, 1981 & Rome, Italy, June 29-July 3, 1981) (pp. 107-122). (Lecture Notes in Control and Information Sciences; Vol. 39). Springer. https://doi.org/10.1007/BFb0006823

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author = "M.L.J. Hautus",

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language = "English",

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editor = "D. Hinrichsen and A. Isidori",

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Hautus, MLJ 1982, Controlled invariance in systems over rings. in D Hinrichsen & A Isidori (eds), Feedback Control of Linear and Nonlinear Systems (Proceedings of the Joint Workshop, Bielefeld, Germany, June 22-26, 1981 & Rome, Italy, June 29-July 3, 1981). Lecture Notes in Control and Information Sciences, vol. 39, Springer, Berlin, pp. 107-122. https://doi.org/10.1007/BFb0006823

Controlled invariance in systems over rings. / Hautus, M.L.J.
Feedback Control of Linear and Nonlinear Systems (Proceedings of the Joint Workshop, Bielefeld, Germany, June 22-26, 1981 & Rome, Italy, June 29-July 3, 1981). ed. / D. Hinrichsen; A. Isidori. Berlin: Springer, 1982. p. 107-122 (Lecture Notes in Control and Information Sciences; Vol. 39).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - The definition of controlled invariant (i.e. (A,B)-invariant) subspaces of a linear system is extended to systems over rings. It is observed that in this more general setting, the equivalence of the geometric and the feedback characterization is no longer true. Particular attention is paid to the weakly unobservable space V*, and conditions are given for this space to satisfy the feedback characterization. These conditions have the form of the existence of a factorization of the transfer function. An application to the disturbance rejection problem is given.

AB - The definition of controlled invariant (i.e. (A,B)-invariant) subspaces of a linear system is extended to systems over rings. It is observed that in this more general setting, the equivalence of the geometric and the feedback characterization is no longer true. Particular attention is paid to the weakly unobservable space V*, and conditions are given for this space to satisfy the feedback characterization. These conditions have the form of the existence of a factorization of the transfer function. An application to the disturbance rejection problem is given.

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BT - Feedback Control of Linear and Nonlinear Systems (Proceedings of the Joint Workshop, Bielefeld, Germany, June 22-26, 1981 & Rome, Italy, June 29-July 3, 1981)

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PB - Springer

CY - Berlin

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Controlled invariance in systems over rings

Abstract

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