Feedback Designs in Information-Based Control

This paper reports a tight bound on the data capacity a feedback channel must provide in order to stabilize a right half-plane pole of a linear, time-invariant control system. The proof is constructive, and involves considering a general class of quantized control realizations of classical feedback designs. Even for the coarsest quantizations—with two-element control input sets, which we refer to as a binary realization—the bound is achievable in the scalar case. The open question of whether bounded trajectories in higher order systems could be produced by a binary realization is answered in the affirmative—again via an explicit construction for a system with two-dimensional state space. It is also shown how binary realizations of classical feedback designs organize the way in which the controller pays attention to different open-loop modes in the plant.