Fundamental Limitations in Control over a Communication Channel

Rojas, A.J. and Braslavsky, J.H. and Middleton, R.H. (2008) Fundamental Limitations in Control over a Communication Channel. Automatica, 44 (12). pp. 3147-3151. ISSN 0005-1098

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Fundamental limitations in feedback control is a well established area of research. In recent years it has been extended to the study of limitations imposed by the consideration of a communication channel in the control loop. Previous results characterised these limitations in terms of a minimal data transmission rate necessary for stabilisation. In this paper a signal-to-noise ratio (SNR) approach is used to obtain a tight condition for the linear time invariant output feedback stabilisation of a continuous-time, unstable, non minimum phase (NMP) plant with time-delay over an additive Gaussian coloured noise communication channel. By working on a linear setting the infimal SNR for stabilisability is defined as the infimal achievable H2 norm between the channel noise input and the channel signal input. The result gives a guideline in estimating the severity of the fundamental SNR limitation imposed by the plant unstable poles, NMP zeros, time-delay as well as the channel NMP zeros, bandwidth, and channel noise colouring.

Item Type: Article
Additional Information: Preprint version of original published article. The definitive version of this article is available at
Keywords: Fundamental constraints; H2 norm; Signal-to-noise ratio; Networks; Input–output stability;
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID: 3522
Depositing User: Hamilton Editor
Date Deposited: 06 Mar 2012 16:32
Journal or Publication Title: Automatica
Publisher: Elsevier
Refereed: No

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