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  Balanced truncation for linear switched systems

Gosea, I. V., Petreczky, M., Antoulas, A. C., & Fiter, C. (2018). Balanced truncation for linear switched systems. Advances in Computational Mathematics, 44(6), 1845-1886. doi:10.1007/s10444-018-9610-z.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0000-2C09-6 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-B30F-4
Genre: Journal Article

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© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0

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 Creators:
Gosea, Ion Victor1, Author              
Petreczky, Mihaly, Author
Antoulas, Athanasios C.1, Author              
Fiter, Christophe, Author
Affiliations:
1Max Planck Fellow Group for Data-Driven System Reduction and Identification, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society, ou_2453691              

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Free keywords: Mathematics, Numerical Analysis, math.NA,cs.SY,
 Abstract: We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode. In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians.

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 Dates: 2018
 Publication Status: Published in print
 Pages: 35 pages, 5 figure, submitted to a special issue journal
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1007/s10444-018-9610-z
URI: http://arxiv.org/abs/1712.02158
arXiv: 1712.02158
Other: pubdata_escidoc:2525657
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Title: Advances in Computational Mathematics
Source Genre: Journal
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Pages: - Volume / Issue: 44 (6) Sequence Number: - Start / End Page: 1845 - 1886 Identifier: ISSN: 1019-7168