Controller Reduction by Krylov Projection Methods

and K(s) = [ AK BK CK DK ] be an n κ order controller with transfer function K(s) = CK(sI − AK)−1BK + DK . We seek a reduced-order controller Kr(s) of order r with r nκ to replace K(s). Assume that both G(s) and K(s) are single-input single-output (SIS0), and that K(s) is a stable stabilizing controller. (The general case follows simply and will be presented in the full paper.) Requiring Kr(s) to be a good approximation to K(s) is often not enough to preserve the desired closed-loop performance; and controller reduction requires one to take plant dynamics into account. This is generally achieved through frequency weighting [1, 9, 8]: Given a stable stabilizing controller K(s), find a stable reduced-order controller Kr(s) so that the weighted error ‖Wo(s)(K(s)−Kr(s))Wi(s)‖H∞ is minimized. To ensure closed-loop stability, one chooses