A Note on the Order of l1-Optimal Compensators

D. Meyer and S. Boyd

Proceedings IEEE Conference on Decision and Control, Athens, Greece, 1:14-15, December 1986.

Recently, Dahleh and Pearson showed that when an l1 optimal compensator for a digital single-input, single-output, time-invariant plant exists, it is rational if the plant itself is. In this note, we give an example of a one-parameter family of first order plants where the order of the optimal compensator can be arbitrarily large. However, computional experience suggests that nearly optimal controllers of reasonable degree usually exist.