Balanced truncation for linear switched systems

Gosea, Ion Victor; Petreczky, Mihaly; Antoulas, Athanasios C.; Fiter, Christophe

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s10444-018-9610-z

Title :

Balanced truncation for linear switched systems

Author(s) :

Gosea, Ion Victor [Auteur]
Max Planck Institute for Dynamics of Complex Technical Systems
Petreczky, Mihaly [Auteur]

Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Systèmes Non Linéaires et à Retards [SyNeR]
Antoulas, Athanasios C. [Auteur]
Max Planck Institute for Dynamics of Complex Technical Systems
Rice University [Houston]
Fiter, Christophe [Auteur]

Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Systèmes Non Linéaires et à Retards [SyNeR]

Journal title :

Advances in Computational Mathematics

Publisher :

Springer Verlag

Publication date :

2018

ISSN :

1019-7168

HAL domain(s) :

Informatique [cs]/Automatique

English abstract : [en]

We propose a model order reduction approach for balanced truncation of linear switchedsystems. Such systems switch among a finite number of linear subsystems or modes.We compute pairs of controllability and observability ...
Show more >We propose a model order reduction approach for balanced truncation of linear switchedsystems. Such systems switch among a finite number of linear subsystems or modes.We compute pairs of controllability and observability Gramians corresponding to each activediscrete mode by solving systems of coupled Lyapunov equations. Depending on the type,each such Gramian corresponds to the energy associated to all possible switching scenariosthat start or, respectively end, in a particular operational mode.In order to guarantee that hard to control and hard to observe states are simultaneouslyeliminated, we construct a transformed system, whose Gramians are equal and diagonal.Then, by truncation, directly construct reduced order models. One can show that thesemodels preserve some properties of the original model, such as stability and that it is possibleto obtain error bounds relating the observed output, the control input and the entries of thediagonal Gramians.Show less >

Language :

Anglais

Popular science :

Non

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