# Dynamic pole assignment and Schubert calculus

Ravi, M; Rosenthal, J; Wang, X (1996). Dynamic pole assignment and Schubert calculus. SIAM Journal on Control and Optimization, 34(3):813-832.

## Abstract

The output feedback pole assignment problem is a classical problem in linear systems theory. In this paper we calculate the number of complex dynamic compensators of order $q$ assigning a given set of poles for a $q$-nondegenerate $m$-input, $p$-output system of McMillan degree $n = q(m + p - 1) + mp$. As a corollary it follows that when this number is odd, the generic system can be arbitrarily pole assigned by output feedback with a real dynamic compensator of order at most $q$ if and only if $q(m + p - 1) + mp \geq n$. ©1996 Society for Industrial and Applied Mathematics

The output feedback pole assignment problem is a classical problem in linear systems theory. In this paper we calculate the number of complex dynamic compensators of order $q$ assigning a given set of poles for a $q$-nondegenerate $m$-input, $p$-output system of McMillan degree $n = q(m + p - 1) + mp$. As a corollary it follows that when this number is odd, the generic system can be arbitrarily pole assigned by output feedback with a real dynamic compensator of order at most $q$ if and only if $q(m + p - 1) + mp \geq n$. ©1996 Society for Industrial and Applied Mathematics

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20 citations in Web of Science®
23 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics output feedback pole assignment, dynamic compensator, holomorphic curves in Grassmannian, degree of variety English 1996 16 Mar 2010 11:24 05 Apr 2016 13:27 Society for Industrial and Applied Mathematics 0363-0129 https://doi.org/10.1137/S036301299325270X
Permanent URL: https://doi.org/10.5167/uzh-22554