Signal-to-Noise Ratio Stability Analysis Subject to Variable Transmission Delay

In this letter we study the effect of an additive white noise (AWN) channel, with a variable transmission time delay, on the stability of a discrete time linear time invariant control feedback loop. The analysis proposes first the use of a buffer, for the received transmissions, of length equal to t...

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Published inIEEE control systems letters Vol. 9; pp. 1375 - 1380
Main Authors Rojas, Alejandro J., Barbosa, Karina
Format Journal Article
LanguageEnglish
Published IEEE 2025
Subjects
Channel models
Delay effects
Delays
Fading channels
Feedback loop
Linear systems
Lower bound
Networked control systems
optimal control
Signal to noise ratio
Stability criteria
Uncertainty
variable transmission delay
Online AccessGet full text
ISSN2475-1456
2475-1456
DOI10.1109/LCSYS.2025.3578276

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Abstract In this letter we study the effect of an additive white noise (AWN) channel, with a variable transmission time delay, on the stability of a discrete time linear time invariant control feedback loop. The analysis proposes first the use of a buffer, for the received transmissions, of length equal to the maximum expected variable transmission delay, when each transmission can be time stamped. Alternatively, we propose modeling the AWN channel variable transmission delay as a sequence of erasure processes, representing the probability of one sample delay, two samples delay, etc., up to the maximum expected transmission delay, when the time stamping of each transmission is not possible. The overall stability of the control feedback loop is then analyzed, for both cases, in terms of the resulting communication channel signal-to-noise ratio (SNR). The second scenario, for treating the variable transmission time delay, results in a more demanding SNR for stability.
AbstractList In this letter we study the effect of an additive white noise (AWN) channel, with a variable transmission time delay, on the stability of a discrete time linear time invariant control feedback loop. The analysis proposes first the use of a buffer, for the received transmissions, of length equal to the maximum expected variable transmission delay, when each transmission can be time stamped. Alternatively, we propose modeling the AWN channel variable transmission delay as a sequence of erasure processes, representing the probability of one sample delay, two samples delay, etc., up to the maximum expected transmission delay, when the time stamping of each transmission is not possible. The overall stability of the control feedback loop is then analyzed, for both cases, in terms of the resulting communication channel signal-to-noise ratio (SNR). The second scenario, for treating the variable transmission time delay, results in a more demanding SNR for stability.
Author Rojas, Alejandro J.
Barbosa, Karina
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  surname: Barbosa
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  email: karina.barbosa@usach.cl
  organization: Department of Electrical Engineering, Universidad de Santiago de Chile, Santiago, Chile
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Snippet In this letter we study the effect of an additive white noise (AWN) channel, with a variable transmission time delay, on the stability of a discrete time...
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StartPage 1375
SubjectTerms Channel models
Delay effects
Delays
Fading channels
Feedback loop
Linear systems
Lower bound
Networked control systems
optimal control
Signal to noise ratio
Stability criteria
Uncertainty
variable transmission delay
Title Signal-to-Noise Ratio Stability Analysis Subject to Variable Transmission Delay
URI https://ieeexplore.ieee.org/document/11029022
Volume 9
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