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Effects of Time Delay on Feedback Stabilisation over Signal-to-Noise Ratio Constrained Channels

Authors:Braslavsky Julio, The University of Newcastle, Australia
Middleton Richard, The University of Newcastle, Australia
Freudenberg James, University of Michigan, Ann Arbor, United States
Topic:2.2 Linear Control Systems
Session:Control of Linear Systems I
Keywords: Communication channels, Feedback stabilisation, Signal-to-noise ratio, Time delay, LQG control.

Abstract

The expanding integration of control and communication networks in recent years has generated an increasing interest in control problems with feedback over a communication channel. Significant research activity has concentrated on stabilisation in face of channel effects such as quantisation and data-rate limits. In a recent paper, the authors have studied the problem of feedback stabilisation over a communication channel with a constraint on the admissible signal-to-noise ratio (SNR). It has been shown therein that for a delay-free, linear time-invariant feedback loop, a SNR constraint in the feedback channel imposes fundamental limitations in the ability to achieve closed-loop stability. The present paper extends these results by introducing a time-delay in the loop, and shows that the lowest SNR required for closed-loop stability increases by a factor that may grow exponentially with the time-delay and the unstable open loop poles of the system. This result contributes to the quantification of performance tradeoffs in integrated control and communication environments.