Pole structure assignment via non-regular static state feedback
type: Item
instance of: scholarly article
title: Pole structure assignment via non-regular static state feedback
zbMATH Open document ID: 0959.93023
DOI: 10.1016/S0005-1098(99)00065-5
published in: Automatica
publication date: 2001-05-02T00:00:00Z
review text: The authors study the problem of transmission pole structure assignment by the non-regular static state feedback \(u= Fx+ Gv\) for linear, time-invariant systems \(\dot x= Ax+ Bu\), where \(A\), \(B\), \(F\), \(G\) are real matrices. They prove a necessary and sufficient condition for a given list of polynomials \(\psi_1(s)\geq \psi_2(s)\geq\cdots\geq \psi_p(s)\) to give the transmission pole structure of the closed-loop system \(\dot x= (A+ BF)x+ BGv\). The condition involves the calculation of the infimal set of the controllability indices the system can attain through feedback while satisfying the Rosenbrock inequalities. The authors use some lattice properties of finite lists of integers to solve the problem.
Mathematics Subject Classification ID: 93B55
zbMATH DE Number: 1353723
zbMATH Keywords: lattice of integer partitions
zbMATH Keywords: pole structure assignment
zbMATH Keywords: non-regular static state feedback
zbMATH Keywords: transmission pole structure
zbMATH Keywords: infimal set of the controllability indices
author: Jean-Jacques Loiseau
author: Petr Zagalak
author: Vladimír Kučera
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
full work available at URL: s0005-1098(99)00065-5
OpenAlex ID: W1995493931
Wikidata QID: Q128066609
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description: scientific article; zbMATH DE number 1353723