Robust stability and performance of stochastic uncertain systems on an infinite time interval

V. A. Ugrinovskii; I. R. Petersen

doi:10.1109/CDC.2000.912762

Robust stability and performance of stochastic uncertain systems on an infinite time interval

V. A. Ugrinovskii^*
, I. R. Petersen

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

Abstract

In this paper, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to estimate the level of guaranteed performance for the stochastic uncertain system under consideration. This solution is obtained by solving an algebraic Riccati equation. The corresponding performance bound holds for all admissible uncertainties and is nonconservative.

Original language	English
Title of host publication	Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	217-221
Number of pages	5
Volume	1
ISBN (Print)	0-7803-6638-7
DOIs	https://doi.org/10.1109/CDC.2000.912762
Publication status	Published - Dec 2000
Externally published	Yes
Event	39th IEEE Confernce on Decision and Control - Sydney Convention and Exhibition Centre, Sydney, Australia Duration: 12 Dec 2000 → 15 Dec 2000 https://www.computer.org/csdl/proceedings-article/cdc/2000/00914087/12OmNxveNMD

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISSN (Print)	0743-1546

Conference

Conference	39th IEEE Confernce on Decision and Control
Country/Territory	Australia
City	Sydney
Period	12/12/00 → 15/12/00
Internet address	https://www.computer.org/csdl/proceedings-article/cdc/2000/00914087/12OmNxveNMD

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10.1109/CDC.2000.912762

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Ugrinovskii, V. A., & Petersen, I. R. (2000). Robust stability and performance of stochastic uncertain systems on an infinite time interval. In Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) (Vol. 1, pp. 217-221). (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2000.912762

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title = "Robust stability and performance of stochastic uncertain systems on an infinite time interval",

abstract = "In this paper, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to estimate the level of guaranteed performance for the stochastic uncertain system under consideration. This solution is obtained by solving an algebraic Riccati equation. The corresponding performance bound holds for all admissible uncertainties and is nonconservative.",

author = "Ugrinovskii, \{V. A.\} and Petersen, \{I. R.\}",

year = "2000",

month = dec,

doi = "10.1109/CDC.2000.912762",

language = "English",

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

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "217--221",

booktitle = "Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)",

address = "United States",

note = "39th IEEE Confernce on Decision and Control ; Conference date: 12-12-2000 Through 15-12-2000",

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Ugrinovskii, VA & Petersen, IR 2000, Robust stability and performance of stochastic uncertain systems on an infinite time interval. in Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187). vol. 1, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 217-221, 39th IEEE Confernce on Decision and Control, Sydney, New South Wales, Australia, 12/12/00. https://doi.org/10.1109/CDC.2000.912762

Robust stability and performance of stochastic uncertain systems on an infinite time interval. / Ugrinovskii, V. A.; Petersen, I. R.
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187). Vol. 1 Institute of Electrical and Electronics Engineers Inc., 2000. p. 217-221 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

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AU - Petersen, I. R.

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N2 - In this paper, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to estimate the level of guaranteed performance for the stochastic uncertain system under consideration. This solution is obtained by solving an algebraic Riccati equation. The corresponding performance bound holds for all admissible uncertainties and is nonconservative.

AB - In this paper, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to estimate the level of guaranteed performance for the stochastic uncertain system under consideration. This solution is obtained by solving an algebraic Riccati equation. The corresponding performance bound holds for all admissible uncertainties and is nonconservative.

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ER -

Ugrinovskii VA, Petersen IR. Robust stability and performance of stochastic uncertain systems on an infinite time interval. In Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187). Vol. 1. Institute of Electrical and Electronics Engineers Inc. 2000. p. 217-221. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2000.912762

Robust stability and performance of stochastic uncertain systems on an infinite time interval

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