Robust schur stability and robust H2 performance for uncertain systems with nonlinear parametric uncertainties

Ke You Zhao; Jakob Stoustrup

doi:10.1109/CDC.1996.574328

Robust schur stability and robust H2 performance for uncertain systems with nonlinear parametric uncertainties

Ke You Zhao^*, Jakob Stoustrup

^*Corresponding author for this work

Research output: Contribution to book/anthology/report/conference proceeding › Book chapter › Research › peer-review

Abstract

The problems of robust stability and robust H₂ performance for uncertain discrete time systems with nonlinear parametric uncertainties are addressed. Two fairly general families of state space models depending nonlinearly on one or two uncertain parameters are considered. For these two families explicit expressions for the Schur stability radius and for the H₂ robust performance radius in the case of uncertainties with a single parameter are obtained, and a line search algorithm for the two problems in case of two parameters is provided. For both problems explicit necessary and sufficient conditions are derived. An illustrative example demonstrates the algorithms.

Original language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Editors	Anon
Volume	1
Publisher	IEEE
Publication date	1 Dec 1996
ISBN (Print)	0-7803-3590-2
DOIs	https://doi.org/10.1109/CDC.1996.574328
Publication status	Published - 1 Dec 1996
Event	Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) - Kobe, Jpn Duration: 11 Dec 1996 → 13 Dec 1996

Conference

Conference	Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4)
City	Kobe, Jpn
Period	11/12/1996 → 13/12/1996
Sponsor	IEEE

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title = "Robust schur stability and robust H2 performance for uncertain systems with nonlinear parametric uncertainties",

abstract = "The problems of robust stability and robust H2 performance for uncertain discrete time systems with nonlinear parametric uncertainties are addressed. Two fairly general families of state space models depending nonlinearly on one or two uncertain parameters are considered. For these two families explicit expressions for the Schur stability radius and for the H2 robust performance radius in the case of uncertainties with a single parameter are obtained, and a line search algorithm for the two problems in case of two parameters is provided. For both problems explicit necessary and sufficient conditions are derived. An illustrative example demonstrates the algorithms.",

author = "Zhao, {Ke You} and Jakob Stoustrup",

year = "1996",

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doi = "10.1109/CDC.1996.574328",

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booktitle = "Proceedings of the IEEE Conference on Decision and Control",

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note = "Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) ; Conference date: 11-12-1996 Through 13-12-1996",

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Zhao, KY & Stoustrup, J 1996, Robust schur stability and robust H2 performance for uncertain systems with nonlinear parametric uncertainties. in Anon (ed.), Proceedings of the IEEE Conference on Decision and Control. vol. 1, IEEE, Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4), Kobe, Jpn, 11/12/1996. https://doi.org/10.1109/CDC.1996.574328

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AU - Stoustrup, Jakob

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AB - The problems of robust stability and robust H2 performance for uncertain discrete time systems with nonlinear parametric uncertainties are addressed. Two fairly general families of state space models depending nonlinearly on one or two uncertain parameters are considered. For these two families explicit expressions for the Schur stability radius and for the H2 robust performance radius in the case of uncertainties with a single parameter are obtained, and a line search algorithm for the two problems in case of two parameters is provided. For both problems explicit necessary and sufficient conditions are derived. An illustrative example demonstrates the algorithms.

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Robust schur stability and robust H2 performance for uncertain systems with nonlinear parametric uncertainties

Abstract

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