Generalized gramian based frequency interval model reduction for unstable systems

Ahmad Jazlan; Victor Sreeram; Roberto Togneri; Ha Binh Minh

doi:10.1109/AUCC.2016.7868000

Generalized gramian based frequency interval model reduction for unstable systems

Ahmad Jazlan, Victor Sreeram, Roberto Togneri, Ha Binh Minh

School of Engineering

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

6 Citations (Scopus)

Abstract

Frequency interval controllability and observability gramian matrices are important in order to understand the characteristics of systems which are inherently frequency dependent. Obtaining these frequency interval controllability and observability gramian matrices requires solving a pair of Lyapunov equations. However for certain systems these Lyapunov equations are not solvable. In addition the eigenvalues of the product of the frequency interval controllability and observability gramians may also be complex numbers and therefore these gramians are not applicable to used in the context of model reduction. To overcome these issues, generalized frequency interval controllability and observability gramians are introduced in this paper and the applicability of these generalized gramians to be used in model reduction is demonstrated.

Original language	English
Title of host publication	2016 Australian Control Conference, AuCC 2016
Place of Publication	Australia
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	43-47
Number of pages	5
ISBN (Electronic)	9781922107909
DOIs	https://doi.org/10.1109/AUCC.2016.7868000
Publication status	Published - 1 Mar 2017
Event	2016 Australian Control Conference - Newcastle, Australia Duration: 3 Nov 2016 → 4 Nov 2016

Conference

Conference	2016 Australian Control Conference
Abbreviated title	AUCC 2016
Country/Territory	Australia
City	Newcastle
Period	3/11/16 → 4/11/16

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10.1109/AUCC.2016.7868000

Cite this

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title = "Generalized gramian based frequency interval model reduction for unstable systems",

abstract = "Frequency interval controllability and observability gramian matrices are important in order to understand the characteristics of systems which are inherently frequency dependent. Obtaining these frequency interval controllability and observability gramian matrices requires solving a pair of Lyapunov equations. However for certain systems these Lyapunov equations are not solvable. In addition the eigenvalues of the product of the frequency interval controllability and observability gramians may also be complex numbers and therefore these gramians are not applicable to used in the context of model reduction. To overcome these issues, generalized frequency interval controllability and observability gramians are introduced in this paper and the applicability of these generalized gramians to be used in model reduction is demonstrated.",

keywords = "Controllability and Observability Gramians, Linear Systems, Lyapunov Equations, Model Order Reduction, Unstable Systems",

author = "Ahmad Jazlan and Victor Sreeram and Roberto Togneri and Minh, {Ha Binh}",

year = "2017",

month = mar,

day = "1",

doi = "10.1109/AUCC.2016.7868000",

language = "English",

pages = "43--47",

booktitle = "2016 Australian Control Conference, AuCC 2016",

publisher = "IEEE, Institute of Electrical and Electronics Engineers",

address = "United States",

note = "2016 Australian Control Conference, AUCC 2016 ; Conference date: 03-11-2016 Through 04-11-2016",

}

Jazlan, A, Sreeram, V , Togneri, R & Minh, HB 2017, Generalized gramian based frequency interval model reduction for unstable systems. in 2016 Australian Control Conference, AuCC 2016., 7868000, IEEE, Institute of Electrical and Electronics Engineers, Australia, pp. 43-47, 2016 Australian Control Conference, Newcastle, Australia, 3/11/16. https://doi.org/10.1109/AUCC.2016.7868000

TY - GEN

T1 - Generalized gramian based frequency interval model reduction for unstable systems

AU - Jazlan, Ahmad

AU - Sreeram, Victor

AU - Togneri, Roberto

AU - Minh, Ha Binh

PY - 2017/3/1

Y1 - 2017/3/1

N2 - Frequency interval controllability and observability gramian matrices are important in order to understand the characteristics of systems which are inherently frequency dependent. Obtaining these frequency interval controllability and observability gramian matrices requires solving a pair of Lyapunov equations. However for certain systems these Lyapunov equations are not solvable. In addition the eigenvalues of the product of the frequency interval controllability and observability gramians may also be complex numbers and therefore these gramians are not applicable to used in the context of model reduction. To overcome these issues, generalized frequency interval controllability and observability gramians are introduced in this paper and the applicability of these generalized gramians to be used in model reduction is demonstrated.

AB - Frequency interval controllability and observability gramian matrices are important in order to understand the characteristics of systems which are inherently frequency dependent. Obtaining these frequency interval controllability and observability gramian matrices requires solving a pair of Lyapunov equations. However for certain systems these Lyapunov equations are not solvable. In addition the eigenvalues of the product of the frequency interval controllability and observability gramians may also be complex numbers and therefore these gramians are not applicable to used in the context of model reduction. To overcome these issues, generalized frequency interval controllability and observability gramians are introduced in this paper and the applicability of these generalized gramians to be used in model reduction is demonstrated.

KW - Controllability and Observability Gramians

KW - Linear Systems

KW - Lyapunov Equations

KW - Model Order Reduction

KW - Unstable Systems

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U2 - 10.1109/AUCC.2016.7868000

DO - 10.1109/AUCC.2016.7868000

M3 - Conference paper

AN - SCOPUS:85016955337

SP - 43

EP - 47

BT - 2016 Australian Control Conference, AuCC 2016

PB - IEEE, Institute of Electrical and Electronics Engineers

CY - Australia

T2 - 2016 Australian Control Conference

Y2 - 3 November 2016 through 4 November 2016

ER -

Generalized gramian based frequency interval model reduction for unstable systems

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