Nonlinear H^∞ control: Practicality of implementing the cheap sensor case

In [5] we introduced a recipe for nonlinear H^∞ controllers which takes advantage of extra perfect measurements and stated a theorem to the effect that this controller yielded the best possible "H^∞" performance. Pure state feedback is an extreme situation and we treated cases where all but a few states are measured perfectly. In this article we analyze the computational complexity of the online part of the H^∞ controller described in [5]. This has important practical implications. Our conclusion is that in reasonable circumstances (even without using much cleverness) when the number of unknown states is less than or equal to 2 and the total number of states is less than or equal to 12 the online portion of the recipe with a 1 GHz PC to produce about 100 controller updates per second.