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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 29, Issue 3

# Subspace confinement for switched linear systems

Yilun Shang
Published Online: 2016-07-30 | DOI: https://doi.org/10.1515/forum-2015-0188

## Abstract

In this note, we introduce the asymptotic subspace confinement problem, generalizing the usual concept of convergence in discrete-time linear systems. Instead of precise convergence, subspace confinement only requires the convergence of states to a certain subspace of the state space, offering useful flexibility and applicability. We establish a criterion for deciding the asymptotic subspace confinement, drawing upon a general finiteness result for the infinite product of matrices. Our results indicate that the asymptotic subspace confinement problem is algorithmically decidable when an invariant subspace for the set of matrices and some polytope norms are given.

MSC 2010: 15A03; 15A60; 40A20; 47A30

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Revised: 2016-04-23

Published Online: 2016-07-30

Published in Print: 2017-05-01

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11505127

Funding Source: Science and Technology Commission of Shanghai Municipality

Award identifier / Grant number: 15PJ1408300

The author acknowledges financial support from the National Natural Science Foundation of China (11505127) and the Shanghai Pujiang Program (15PJ1408300).

Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 693–699, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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