A note on the order of l1 optimal compensators

Recently, Dahleh and Pearson [1] 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, computational experience suggests that nearly optimal controllers of reasonable degree usually exist.