Dissipativity based H∞ control for nonlinear stochastic systems with time-varying delays

Huiping Li; Yang Shi

doi:10.1109/CDC.2011.6161318

Dissipativity based H_∞ control for nonlinear stochastic systems with time-varying delays

Huiping Li
, Yang Shi

University of Victoria BC

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

1 Scopus citations

Abstract

This paper is concerned with the H_∞ state feedback control problem for a class of nonlinear stochastic systems with time-varying state delays. Firstly, the stochastic dissipativity of the time-delay nonlinear system is established, based on which the H_∞ state feedback controller is synthesized. We show that the closed-loop system rendered by the designed controller can achieve the L₂-gain performance and exponential stability in the sense of mean square. Finally, these sufficient conditions are further specialized as solving a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) for a class of special stochastic nonlinear delayed systems.

Original language	English
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3240-3245
Number of pages	6
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6161318
State	Published - 2011
Externally published	Yes
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: 12 Dec 2011 → 15 Dec 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 15/12/11

Access to Document

10.1109/CDC.2011.6161318

Cite this

Li, H., & Shi, Y. (2011). Dissipativity based H_∞ control for nonlinear stochastic systems with time-varying delays. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 3240-3245). Article 6161318 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2011.6161318

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title = "Dissipativity based H∞ control for nonlinear stochastic systems with time-varying delays",

abstract = "This paper is concerned with the H∞ state feedback control problem for a class of nonlinear stochastic systems with time-varying state delays. Firstly, the stochastic dissipativity of the time-delay nonlinear system is established, based on which the H∞ state feedback controller is synthesized. We show that the closed-loop system rendered by the designed controller can achieve the L2-gain performance and exponential stability in the sense of mean square. Finally, these sufficient conditions are further specialized as solving a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) for a class of special stochastic nonlinear delayed systems.",

author = "Huiping Li and Yang Shi",

year = "2011",

doi = "10.1109/CDC.2011.6161318",

language = "英语",

isbn = "9781612848006",

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

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

pages = "3240--3245",

booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

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Li, H & Shi, Y 2011, Dissipativity based H_∞ control for nonlinear stochastic systems with time-varying delays. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6161318, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 3240-3245, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161318

Dissipativity based H_∞ control for nonlinear stochastic systems with time-varying delays. / Li, Huiping; Shi, Yang.
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 3240-3245 6161318 (Proceedings of the IEEE Conference on Decision and Control).

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

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AB - This paper is concerned with the H∞ state feedback control problem for a class of nonlinear stochastic systems with time-varying state delays. Firstly, the stochastic dissipativity of the time-delay nonlinear system is established, based on which the H∞ state feedback controller is synthesized. We show that the closed-loop system rendered by the designed controller can achieve the L2-gain performance and exponential stability in the sense of mean square. Finally, these sufficient conditions are further specialized as solving a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) for a class of special stochastic nonlinear delayed systems.

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Li H, Shi Y. Dissipativity based H_∞ control for nonlinear stochastic systems with time-varying delays. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc. 2011. p. 3240-3245. 6161318. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2011.6161318