On Decentralized Dynamic Pole Placement and Feedback Stabilization

M. S. Ravi; Joachim Rosenthal; Xiaochang A. Wang

doi:10.1109/9.412629

On Decentralized Dynamic Pole Placement and Feedback Stabilization

M. S. Ravi, Joachim Rosenthal, Xiaochang A. Wang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

In this paper we study the feedback control problem using an r-channel decentralized dynamic feedback control scheme. We will develop the theory in the behavioral framework. Using this framework we introduce an algebraic parameterization of the space of all possible feedback compensators having a bounded McMillan degree, and we show that this parameterization has the structure of an algebraic variety. We define the pole-placement map for this problem, and we give exact conditions when this map is onto, and almost onto. Finally we provide new necessary and sufficient conditions which guarantee that the set of stabilizable plants is a generic set.

Original language	English
Pages (from-to)	1603-1614
Number of pages	12
Journal	IEEE Transactions on Automatic Control
Volume	40
Issue number	9
DOIs	https://doi.org/10.1109/9.412629
State	Published - Sep 1995

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title = "On Decentralized Dynamic Pole Placement and Feedback Stabilization",

abstract = "In this paper we study the feedback control problem using an r-channel decentralized dynamic feedback control scheme. We will develop the theory in the behavioral framework. Using this framework we introduce an algebraic parameterization of the space of all possible feedback compensators having a bounded McMillan degree, and we show that this parameterization has the structure of an algebraic variety. We define the pole-placement map for this problem, and we give exact conditions when this map is onto, and almost onto. Finally we provide new necessary and sufficient conditions which guarantee that the set of stabilizable plants is a generic set.",

author = "Ravi, {M. S.} and Joachim Rosenthal and Wang, {Xiaochang A.}",

note = "Funding Information: Manuscript received March 25, 1994; revised September 6, 1994 and February 13, 1995. Recommended by Associate Editor, A. A. Stoorvogel. This work was supported in part by NSF Grants DMS-9400965 and DMS-922454 1. M. S. Ravi is with Department of Mathematics, East Carolina University, Greenville, NC 27858 USA. J. Rosenthal is with Depaa{"}nt of Mathematics, University of Notre Dame, Notre Dame, IN 46556-5683 USA. X. Wang is with Department of Mathematics, Texas Tech University, Lubbock, TX 79409 USA. IEEE Log Number 9413528.",

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AU - Wang, Xiaochang A.

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N2 - In this paper we study the feedback control problem using an r-channel decentralized dynamic feedback control scheme. We will develop the theory in the behavioral framework. Using this framework we introduce an algebraic parameterization of the space of all possible feedback compensators having a bounded McMillan degree, and we show that this parameterization has the structure of an algebraic variety. We define the pole-placement map for this problem, and we give exact conditions when this map is onto, and almost onto. Finally we provide new necessary and sufficient conditions which guarantee that the set of stabilizable plants is a generic set.

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On Decentralized Dynamic Pole Placement and Feedback Stabilization

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