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On the stabilizability of multivariable systems by minimum order compensationIn this paper, a derivation is provided of the necessary condition, mp equal to or greater than n, for stabilizability by constant gain feedback of the generic degree n, p x m system. This follows from another of the main results, which asserts that generic stabilizability is equivalent to generic solvability of a deadbeat control problem, provided mp equal to or less than n. Taken together, these conclusions make it possible to make some sharp statements concerning minimum order stabilization. The techniques are primarily drawn from decision algebra and classical algebraic geometry and have additional consequences for problems of stabilizability and pole-assignability. Among these are the decidability (by a Sturm test) of the equivalence of generic pole-assignability and generic stabilizability, the semi-algebraic nature of the minimum order, q, of a stabilizing compensator, and the nonexistence of formulae involving rational operations and extraction of square roots for pole-assigning gains when they exist, answering in the negative a question raised by Anderson, Bose, and Jury (1975).
Document ID
19850051163
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Byrnes, C. I.
(Harvard University Cambridge, MA, United States)
Anderson, B. D. O.
(Australian National University Canberra, Australia)
Date Acquired
August 12, 2013
Publication Date
January 1, 1983
Subject Category
Cybernetics
Meeting Information
Meeting: Conference on Decision and Control
Location: San Antonio, TX
Start Date: December 14, 1983
End Date: December 16, 1983
Sponsors: IEEE
Accession Number
85A33314
Funding Number(s)
CONTRACT_GRANT: NSG-2265
CONTRACT_GRANT: AF-AFOSR-81-0054
CONTRACT_GRANT: NSF ECS-81-21428
Distribution Limits
Public
Copyright
Other

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