Switched systems reduction framework based on convex combination of generalized gramians

Hamid Reza Shaker, Rafael Wisniewski

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

A general method for model-order reduction of switched linear dynamical systems is presented. The proposed technique uses convex generalized gramian which is a convex combination of the generalized gramians. It is shown that different classical reduction methods can be developed into the generalized gramian framework for model reduction of linear systems and further for the reduction of switched systems by construction of the convex generalized gramian. Balanced reduction within specified frequency bound is taken as an example which is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, convex generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the method preserves the stability of the original switched system at least for stabilizing switching signal and it is also less conservative than the method which is based on the common generalized gramian. Some discussions on the coefficient of the vertices of the convex variables are presented. The performance of the proposed method is illustrated by numerical examples.

OriginalsprogEngelsk
Artikelnummer710478
TidsskriftJournal of Control Science and Engineering
Vol/bind2009
ISSN1687-5249
DOI
StatusUdgivet - 1. dec. 2009
Udgivet eksterntJa

Fingeraftryk

Convex Combination
Switched Systems
Model Order Reduction
Petrov-Galerkin
Linear Dynamical Systems
Numerical Instability
Model Reduction
Reduction Method
Linear Systems
Projection
Transform
Numerical Examples
Linear systems
Framework
Dynamical systems
Coefficient

Citer dette

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abstract = "A general method for model-order reduction of switched linear dynamical systems is presented. The proposed technique uses convex generalized gramian which is a convex combination of the generalized gramians. It is shown that different classical reduction methods can be developed into the generalized gramian framework for model reduction of linear systems and further for the reduction of switched systems by construction of the convex generalized gramian. Balanced reduction within specified frequency bound is taken as an example which is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, convex generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the method preserves the stability of the original switched system at least for stabilizing switching signal and it is also less conservative than the method which is based on the common generalized gramian. Some discussions on the coefficient of the vertices of the convex variables are presented. The performance of the proposed method is illustrated by numerical examples.",
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Switched systems reduction framework based on convex combination of generalized gramians. / Shaker, Hamid Reza; Wisniewski, Rafael.

I: Journal of Control Science and Engineering, Bind 2009, 710478, 01.12.2009.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

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AU - Wisniewski, Rafael

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AB - A general method for model-order reduction of switched linear dynamical systems is presented. The proposed technique uses convex generalized gramian which is a convex combination of the generalized gramians. It is shown that different classical reduction methods can be developed into the generalized gramian framework for model reduction of linear systems and further for the reduction of switched systems by construction of the convex generalized gramian. Balanced reduction within specified frequency bound is taken as an example which is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, convex generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the method preserves the stability of the original switched system at least for stabilizing switching signal and it is also less conservative than the method which is based on the common generalized gramian. Some discussions on the coefficient of the vertices of the convex variables are presented. The performance of the proposed method is illustrated by numerical examples.

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