Stabilization and performance over a Gaussian communication channel for a plant with time delay

Authors:
J. S. Freudenberg;R. H. Middleton
Affiliations:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI;Hamilton Institute, National University of Ireland Maynooth, Co. Kildare, Ireland
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

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Abstract

Two problems that have received much attention are those of finding the minimum channel signal to noise ratio compatible with closed loop stability, and of finding the optimal performance, in terms of disturbance attenuation, for a channel with specified signal to noise ratio. In this paper, we study these problems for the case in which the plant has relative degree greater than one, and thus introduces a delay greater than one time step. We show that, unlike the relative degree one case, for the problem of stabilization linear time varying control and communication strategies may have advantages over linear time invariant strategies. We derive a lower bound on optimal disturbance response at a fixed terminal time. If the encoder has access to the state of the plant, then this bound is achievable using linear time varying communication and control.