Rojas, A.J. and Braslavsky, J.H. and Middleton, R.H.
Fundamental Limitations in Control over a Communication Channel.
Automatica, 44 (12).
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.
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