Frequency Interval Cross Gramians for Linear and Bilinear Systems

Ahmad Jazlan, Victor Sreeram, Hamid Reza Shaker, Roberto Togneri, Ha BinhMinh

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians relative to existing methods.
Original languageEnglish
JournalAsian Journal of Control
Volume19
Issue number1
Pages (from-to)22-34
ISSN1561-8625
DOIs
Publication statusPublished - 2017

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Observability
Controllability
Computational efficiency

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Jazlan, Ahmad ; Sreeram, Victor ; Shaker, Hamid Reza ; Togneri, Roberto ; BinhMinh , Ha . / Frequency Interval Cross Gramians for Linear and Bilinear Systems. In: Asian Journal of Control. 2017 ; Vol. 19, No. 1. pp. 22-34.
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Frequency Interval Cross Gramians for Linear and Bilinear Systems. / Jazlan, Ahmad; Sreeram, Victor ; Shaker, Hamid Reza; Togneri, Roberto ; BinhMinh , Ha .

In: Asian Journal of Control, Vol. 19, No. 1, 2017, p. 22-34.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Frequency Interval Cross Gramians for Linear and Bilinear Systems

AU - Jazlan, Ahmad

AU - Sreeram, Victor

AU - Shaker, Hamid Reza

AU - Togneri, Roberto

AU - BinhMinh , Ha

PY - 2017

Y1 - 2017

N2 - In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians relative to existing methods.

AB - In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians relative to existing methods.

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DO - 10.1002/asjc.1330

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JO - Asian Journal of Control

JF - Asian Journal of Control

SN - 1561-8625

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