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New results in pole assignment by real output feedback


Rosenthal, J (1992). New results in pole assignment by real output feedback. SIAM Journal on Control and Optimization, 30(1):203-211.

Abstract

This paper considers the problem of tuning natural frequencies of a linear system by a memoryless controller. Using algebro-geometric methods it is shown how it is possible to improve current sufficiency conditions.The main result is an exact combinatorial characterization of the nilpotency index of the $\bmod 2$ cohomology ring of the real Grassmannian. Using this characterization, new sufficiency results for generic pole assignment for the linear system with $m$-inputs, $p$-outputs, and McMillan degree $n$ are given. Among other results it is shown that \[2.25 \cdot \max (m,p) + \min (m,p) - 3 \geq n\] is a sufficient condition for generic real pole placement, provided $\min (m,p) \geq 4$. ©1992 Society for Industrial and Applied Mathematics

This paper considers the problem of tuning natural frequencies of a linear system by a memoryless controller. Using algebro-geometric methods it is shown how it is possible to improve current sufficiency conditions.The main result is an exact combinatorial characterization of the nilpotency index of the $\bmod 2$ cohomology ring of the real Grassmannian. Using this characterization, new sufficiency results for generic pole assignment for the linear system with $m$-inputs, $p$-outputs, and McMillan degree $n$ are given. Among other results it is shown that \[2.25 \cdot \max (m,p) + \min (m,p) - 3 \geq n\] is a sufficient condition for generic real pole placement, provided $\min (m,p) \geq 4$. ©1992 Society for Industrial and Applied Mathematics

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:output feedback, pole placement, intersection theory, symmetric functions
Language:English
Date:1992
Deposited On:22 Mar 2010 16:09
Last Modified:05 Apr 2016 13:28
Publisher:Society for Industrial and Applied Mathematics
ISSN:0363-0129
Additional Information:First published in SIAM J. Control Optim. 30 (1992), no. 1, published by the American Mathematical Society
Publisher DOI:https://doi.org/10.1137/0330013
Permanent URL: https://doi.org/10.5167/uzh-22737

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