Finite frequency negative imaginary systems

Junlin Xiong; Ian R. Petersen; Alexander Lanzon

doi:10.1109/TAC.2012.2193705

Finite frequency negative imaginary systems

Junlin Xiong, Ian R. Petersen, Alexander Lanzon

Research output: Contribution to journal › Article › peer-review

Abstract

This technical note is concerned with finite frequency negative imaginary (FFNI) systems. Firstly, the concept of FFNI transfer function matrices is introduced, and the relationship between the FFNI property and the finite frequency positive real property of transfer function matrices is studied. Then the technical note establishes an FFNI lemma which gives a necessary and sufficient condition on matrices appearing in a minimal state-space realization for a transfer function to be FFNI. Also, a time-domain interpretation of the FFNI property is provided in terms of the system input, output and state. Finally, an example is presented to illustrate the FFNI concept and the FFNI lemma. © 2012 IEEE.

Original language	English
Article number	6187701
Pages (from-to)	1917-1922
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	57
Issue number	11
DOIs	https://doi.org/10.1109/TAC.2012.2193705
Publication status	Published - 2012

Keywords

Lightly damped systems
negative imaginary systems
positive real systems

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10.1109/TAC.2012.2193705

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title = "Finite frequency negative imaginary systems",

abstract = "This technical note is concerned with finite frequency negative imaginary (FFNI) systems. Firstly, the concept of FFNI transfer function matrices is introduced, and the relationship between the FFNI property and the finite frequency positive real property of transfer function matrices is studied. Then the technical note establishes an FFNI lemma which gives a necessary and sufficient condition on matrices appearing in a minimal state-space realization for a transfer function to be FFNI. Also, a time-domain interpretation of the FFNI property is provided in terms of the system input, output and state. Finally, an example is presented to illustrate the FFNI concept and the FFNI lemma. {\textcopyright} 2012 IEEE.",

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author = "Junlin Xiong and Petersen, {Ian R.} and Alexander Lanzon",

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AU - Petersen, Ian R.

AU - Lanzon, Alexander

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AB - This technical note is concerned with finite frequency negative imaginary (FFNI) systems. Firstly, the concept of FFNI transfer function matrices is introduced, and the relationship between the FFNI property and the finite frequency positive real property of transfer function matrices is studied. Then the technical note establishes an FFNI lemma which gives a necessary and sufficient condition on matrices appearing in a minimal state-space realization for a transfer function to be FFNI. Also, a time-domain interpretation of the FFNI property is provided in terms of the system input, output and state. Finally, an example is presented to illustrate the FFNI concept and the FFNI lemma. © 2012 IEEE.

KW - Lightly damped systems

KW - negative imaginary systems

KW - positive real systems

U2 - 10.1109/TAC.2012.2193705

DO - 10.1109/TAC.2012.2193705

M3 - Article

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EP - 1922

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 11

M1 - 6187701

ER -

Finite frequency negative imaginary systems

Abstract

Keywords

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