- Title
- Signal-to-noise ratio fundamental limitations in continuous-time linear output feedback control
- Creator
- Rojas, Alejandro J.
- Relation
- IEEE Transactions on Automatic Control Vol. 54, Issue 8, p. 1902-1907
- Publisher Link
- http://dx.doi.org/10.1109/TAC.2009.2022114
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2009
- Description
- In the present technical note we study the fundamental limitation on stability that arise when an additive coloured Gaussian noise (ACGN) channel is explicitly considered over either the control or measurement paths of a linear time invariant (LTI) feedback loop. By considering a linear setting we can naturally express the fundamental limitation as a lower bound on the channel signal-to-noise ratio (SNR) required for stabilisability. We start by first obtaining a closed-form expression for the squared L₂ norm of a partial fraction expansion with repeated poles in the Laplace domain. We then use the squared L₂ norm result to obtain the closed-form expression for the infimal SNR required for stabilisability. The proposed closed-form includes the case of repeated unstable plant poles and non minimum phase (NMP) zeros.
- Subject
- additive coloured Gaussian noise (ACGN); signal-to-noise ratio (SNR)
- Identifier
- http://hdl.handle.net/1959.13/808855
- Identifier
- uon:7766
- Identifier
- ISSN:0018-9286
- Rights
- Copyright © 2009 IEEE. Reprinted from the IEEE Transactions on Automatic Control Vol. 54, Issue 8, p. 1902-1907. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
- Language
- eng
- Full Text
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