Algebraic and topological aspects of feedback stabilization

Vidyasagar, M. ; Schneider, H. ; Francis, B. (1982) Algebraic and topological aspects of feedback stabilization IEEE Transactions on Automatic Control, 27 (4). pp. 880-894. ISSN 0018-9286

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In this paper we give essentially complete results concerning various algebraic and topological aspects of feedback stabilization. In particular, we give necessary and sufficient conditions for a given transfer function matrix to have a right-coprime or a left-coprime factorization, and exhibit a large class of transfer function matrices that have both. We give the most general set of feedback stability criteria available to date, and derive a characterization of all compensators that stabilize a given plant. We give a definition of "proper" and "strictly proper" in an abstract setting and show that 1) ever strictly proper plant can be stabilized by a proper compensator, and 2) every compensator that stabilizes a strictly proper plant must be proper. We then define a topology for unstable plants and compensators, and show that it is the weakest topology in which feedback stability is a robust property.

Item Type:Article
Source:Copyright of this article belongs to IEEE.
ID Code:56176
Deposited On:22 Aug 2011 12:37
Last Modified:22 Aug 2011 12:37

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