Balanced truncation for linear switched systems
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Balanced truncation for linear switched systems
Auteur(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]
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]
Titre de la revue :
Advances in Computational Mathematics
Éditeur :
Springer Verlag
Date de publication :
2018
ISSN :
1019-7168
Discipline(s) HAL :
Informatique [cs]/Automatique
Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Collections :
Source :
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