Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition

Hiroshi Ito; Pierdomenico Pepe; Zhong Ping Jiang

doi:10.1109/CDC.2009.5399840

Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition

Hiroshi Ito, Pierdomenico Pepe, Zhong Ping Jiang

Electrical and Computer Engineering

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

Abstract

This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain theorem for the interconnection of these components to assess the stability of the overall time-delay system. Both discrete and distributed delays can be involved in the dynamic and the static components. The result can be considered as a counterpart of the author's previous work which only deals with dynamic components. For the construction of Lyapunov-Krasovskii functionals, this paper introduces a new technique which differs from the one employed in the dynamic case.

Original language	English (US)
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1310-1316
Number of pages	7
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399840
State	Published - 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: Dec 15 2009 → Dec 18 2009

Publication series

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

Other

Other	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	12/15/09 → 12/18/09

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2009.5399840

Cite this

Ito, H., Pepe, P., & Jiang, Z. P. (2009). Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 1310-1316). Article 5399840 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399840

Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition. / Ito, Hiroshi; Pepe, Pierdomenico; Jiang, Zhong Ping.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 1310-1316 5399840 (Proceedings of the IEEE Conference on Decision and Control).

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

Ito, H, Pepe, P & Jiang, ZP 2009, Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399840, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 1310-1316, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5399840

Ito H, Pepe P, Jiang ZP. Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 1310-1316. 5399840. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5399840

Ito, Hiroshi ; Pepe, Pierdomenico ; Jiang, Zhong Ping. / Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 1310-1316 (Proceedings of the IEEE Conference on Decision and Control).

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abstract = "This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain theorem for the interconnection of these components to assess the stability of the overall time-delay system. Both discrete and distributed delays can be involved in the dynamic and the static components. The result can be considered as a counterpart of the author's previous work which only deals with dynamic components. For the construction of Lyapunov-Krasovskii functionals, this paper introduces a new technique which differs from the one employed in the dynamic case.",

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AB - This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain theorem for the interconnection of these components to assess the stability of the overall time-delay system. Both discrete and distributed delays can be involved in the dynamic and the static components. The result can be considered as a counterpart of the author's previous work which only deals with dynamic components. For the construction of Lyapunov-Krasovskii functionals, this paper introduces a new technique which differs from the one employed in the dynamic case.

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Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition

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