Model reduction of switched systems based on switching generalized gramians

Hamid Reza Shaker, Rafael Wisniewski

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper, a general method for model order reduction of discrete-time switched linear systems is presented. The proposed technique uses switching generalized gramians. It is shown that several classical reduction methods can be developed into the generalized gramian framework for the model reduction of linear systems and for the reduction of switched systems. Discrete-time balanced reduction within a specified frequency interval is taken as an example within this framework. To avoid numerical instability and to increase the numerical efficiency, a generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the proposed reduction framework preserves the stability of the original switched system. The performance of the method is illustrated by numerical examples.

Original languageEnglish
JournalInternational Journal of Innovative Computing, Information and Control
Volume8
Issue number7 B
Pages (from-to)5025-5044
Number of pages20
ISSN1349-4198
Publication statusPublished - 1. Jul 2012
Externally publishedYes

Fingerprint

Switched Systems
Model Reduction
Discrete-time
Model Order Reduction
Switched Linear Systems
Petrov-Galerkin
Numerical Instability
Reduction Method
Linear systems
Linear Systems
Projection
Transform
Numerical Examples
Interval
Framework

Keywords

  • Gramian and stability
  • Model reduction
  • Switched systems

Cite this

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abstract = "In this paper, a general method for model order reduction of discrete-time switched linear systems is presented. The proposed technique uses switching generalized gramians. It is shown that several classical reduction methods can be developed into the generalized gramian framework for the model reduction of linear systems and for the reduction of switched systems. Discrete-time balanced reduction within a specified frequency interval is taken as an example within this framework. To avoid numerical instability and to increase the numerical efficiency, a generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the proposed reduction framework preserves the stability of the original switched system. The performance of the method is illustrated by numerical examples.",
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Model reduction of switched systems based on switching generalized gramians. / Shaker, Hamid Reza; Wisniewski, Rafael.

In: International Journal of Innovative Computing, Information and Control, Vol. 8, No. 7 B, 01.07.2012, p. 5025-5044.

Research output: Contribution to journalJournal articleResearchpeer-review

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T1 - Model reduction of switched systems based on switching generalized gramians

AU - Shaker, Hamid Reza

AU - Wisniewski, Rafael

PY - 2012/7/1

Y1 - 2012/7/1

N2 - In this paper, a general method for model order reduction of discrete-time switched linear systems is presented. The proposed technique uses switching generalized gramians. It is shown that several classical reduction methods can be developed into the generalized gramian framework for the model reduction of linear systems and for the reduction of switched systems. Discrete-time balanced reduction within a specified frequency interval is taken as an example within this framework. To avoid numerical instability and to increase the numerical efficiency, a generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the proposed reduction framework preserves the stability of the original switched system. The performance of the method is illustrated by numerical examples.

AB - In this paper, a general method for model order reduction of discrete-time switched linear systems is presented. The proposed technique uses switching generalized gramians. It is shown that several classical reduction methods can be developed into the generalized gramian framework for the model reduction of linear systems and for the reduction of switched systems. Discrete-time balanced reduction within a specified frequency interval is taken as an example within this framework. To avoid numerical instability and to increase the numerical efficiency, a generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the proposed reduction framework preserves the stability of the original switched system. The performance of the method is illustrated by numerical examples.

KW - Gramian and stability

KW - Model reduction

KW - Switched systems

M3 - Journal article

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JO - International Journal of Innovative Computing, Information and Control

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