Decentralized stabilization of interconnected systems with time-varying delays

Magdi S. Mahmoud

doi:10.1109/TAC.2009.2031572

Decentralized stabilization of interconnected systems with time-varying delays

Magdi S. Mahmoud

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

87 Scopus citations

Abstract

This technical note establishes decentralized delay-dependent stability and stabilization methods for two classes of interconnected continuous-time systems. The two classes cover the linear case and the Lipschitz-type nonlinear case. In both cases, the subsystems are subjected to convex-bounded parametric uncertainties and time-varying delays within the local subsystems and across the interconnections. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics at the subsystem level. In both cases, decentralized delay-dependent stability analysis is performed to characterize linear matrix inequalities (LMIs)-based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an-γ-level L₂-gain. Then we design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent asymptotic stability with a prescribed γ-level L₂gain for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example.

Original language	English
Article number	5286276
Pages (from-to)	2663-2668
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	54
Issue number	11
DOIs	https://doi.org/10.1109/TAC.2009.2031572
State	Published - Nov 2009

Bibliographical note

Funding Information:
Manuscript received April 22, 2008; revised May 30, 2009. First published October 13, 2009; current version published November 04, 2009. This work was supported by KFUPM under Project FT-090015. Recommended by Associate Editor P. A. Parrilo.

Keywords

Decentralized stabilization
Delay-dependent stability
Interconnected systems
Linear matrix inequalities (LMIs)
Time-delay systems

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2009.2031572

Cite this

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title = "Decentralized stabilization of interconnected systems with time-varying delays",

abstract = "This technical note establishes decentralized delay-dependent stability and stabilization methods for two classes of interconnected continuous-time systems. The two classes cover the linear case and the Lipschitz-type nonlinear case. In both cases, the subsystems are subjected to convex-bounded parametric uncertainties and time-varying delays within the local subsystems and across the interconnections. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics at the subsystem level. In both cases, decentralized delay-dependent stability analysis is performed to characterize linear matrix inequalities (LMIs)-based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an-γ-level L2-gain. Then we design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent asymptotic stability with a prescribed γ-level L2gain for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example.",

keywords = "Decentralized stabilization, Delay-dependent stability, Interconnected systems, Linear matrix inequalities (LMIs), Time-delay systems",

author = "Mahmoud, \{Magdi S.\}",

note = "Funding Information: Manuscript received April 22, 2008; revised May 30, 2009. First published October 13, 2009; current version published November 04, 2009. This work was supported by KFUPM under Project FT-090015. Recommended by Associate Editor P. A. Parrilo.",

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AU - Mahmoud, Magdi S.

N1 - Funding Information: Manuscript received April 22, 2008; revised May 30, 2009. First published October 13, 2009; current version published November 04, 2009. This work was supported by KFUPM under Project FT-090015. Recommended by Associate Editor P. A. Parrilo.

PY - 2009/11

Y1 - 2009/11

N2 - This technical note establishes decentralized delay-dependent stability and stabilization methods for two classes of interconnected continuous-time systems. The two classes cover the linear case and the Lipschitz-type nonlinear case. In both cases, the subsystems are subjected to convex-bounded parametric uncertainties and time-varying delays within the local subsystems and across the interconnections. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics at the subsystem level. In both cases, decentralized delay-dependent stability analysis is performed to characterize linear matrix inequalities (LMIs)-based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an-γ-level L2-gain. Then we design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent asymptotic stability with a prescribed γ-level L2gain for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example.

AB - This technical note establishes decentralized delay-dependent stability and stabilization methods for two classes of interconnected continuous-time systems. The two classes cover the linear case and the Lipschitz-type nonlinear case. In both cases, the subsystems are subjected to convex-bounded parametric uncertainties and time-varying delays within the local subsystems and across the interconnections. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics at the subsystem level. In both cases, decentralized delay-dependent stability analysis is performed to characterize linear matrix inequalities (LMIs)-based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an-γ-level L2-gain. Then we design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent asymptotic stability with a prescribed γ-level L2gain for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example.

KW - Decentralized stabilization

KW - Delay-dependent stability

KW - Interconnected systems

KW - Linear matrix inequalities (LMIs)

KW - Time-delay systems

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DO - 10.1109/TAC.2009.2031572

M3 - Article

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SP - 2663

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 11

M1 - 5286276

ER -

Decentralized stabilization of interconnected systems with time-varying delays

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this