Robust analysis and synthesis for the nonexistence of periodic solutions in a class of nonlinear systems

P. L. Lu; Y. Yang; L. Huang

doi:10.1007/s10957-007-9241-x

Robust analysis and synthesis for the nonexistence of periodic solutions in a class of nonlinear systems

P. L. Lu^*, Y. Yang, L. Huang

^*Corresponding author for this work

Peking University

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

2 Citations (Scopus)

Abstract

This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of the proposed approach.

Original language	English
Pages (from-to)	205-216
Number of pages	12
Journal	Journal of Optimization Theory and Applications
Volume	135
Issue number	2
DOIs	https://doi.org/10.1007/s10957-007-9241-x
Publication status	Published - Nov 2007
Externally published	Yes

Keywords

GKYP lemma
LMIs
Polytopic uncertainty

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10.1007/s10957-007-9241-x

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title = "Robust analysis and synthesis for the nonexistence of periodic solutions in a class of nonlinear systems",

abstract = "This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of the proposed approach.",

keywords = "GKYP lemma, LMIs, Polytopic uncertainty",

author = "Lu, {P. L.} and Y. Yang and L. Huang",

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T1 - Robust analysis and synthesis for the nonexistence of periodic solutions in a class of nonlinear systems

AU - Lu, P. L.

AU - Yang, Y.

AU - Huang, L.

PY - 2007/11

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N2 - This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of the proposed approach.

AB - This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of the proposed approach.

KW - GKYP lemma

KW - LMIs

KW - Polytopic uncertainty

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IS - 2

ER -

Robust analysis and synthesis for the nonexistence of periodic solutions in a class of nonlinear systems

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Keywords

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