Quantized feedback stabilization of interconnected continuous time-delay systems

Magdi S. Mahmoud; Ali Y. Al-Rayyah; Yuanqing Xia

doi:10.1093/imamci/dnq018

Quantized feedback stabilization of interconnected continuous time-delay systems

Magdi S. Mahmoud, Ali Y. Al-Rayyah, Yuanqing Xia

School of Automation

King Fahd University of Petroleum and Minerals

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

20 Citations (Scopus)

Abstract

In this paper, the problem of quantized feedback stabilization is approached from a generalized setting by designing a decentralized ℋ_∞ feedback control for a class of linear interconnected continuous-time systems with unknown-but-bounded couplings and interval delays and where the quantizer has arbitrary form that satisfies a quadratic inequality constraint. An LMI-based method using a decentralized quantized output-feedback controller is designed at the subsystem level to render the closed-loop system delay-dependent asymptotically stable with guaranteed γ-level. It is established that this setting encompasses several special cases of interest including interconnected delay-free systems, single time-delay systems and single systems. We illustrate the theoretical developments by numerical simulations.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	IMA Journal of Mathematical Control and Information
Volume	28
Issue number	1
DOIs	https://doi.org/10.1093/imamci/dnq018
Publication status	Published - Mar 2011

Keywords

LMIs
delay-dependent stabilization
interconnected time-delay systems
quantized feedback control
quantizer

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10.1093/imamci/dnq018

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Mahmoud, M. S., Al-Rayyah, A. Y., & Xia, Y. (2011). Quantized feedback stabilization of interconnected continuous time-delay systems. IMA Journal of Mathematical Control and Information, 28(1), 1-17. https://doi.org/10.1093/imamci/dnq018

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AB - In this paper, the problem of quantized feedback stabilization is approached from a generalized setting by designing a decentralized ℋ∞ feedback control for a class of linear interconnected continuous-time systems with unknown-but-bounded couplings and interval delays and where the quantizer has arbitrary form that satisfies a quadratic inequality constraint. An LMI-based method using a decentralized quantized output-feedback controller is designed at the subsystem level to render the closed-loop system delay-dependent asymptotically stable with guaranteed γ-level. It is established that this setting encompasses several special cases of interest including interconnected delay-free systems, single time-delay systems and single systems. We illustrate the theoretical developments by numerical simulations.

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Quantized feedback stabilization of interconnected continuous time-delay systems

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