Pj. Goddard et K. Glover, CONTROLLER APPROXIMATION - APPROACHES FOR PRESERVING H-INFINITY PERFORMANCE, IEEE transactions on automatic control, 43(7), 1998, pp. 858-871
This paper investigates the design of reduced-order controllers using
an H-infinity framework. Given a stabilizing controller which satisfie
s a prespecified level of closed-loop H-infinity performance, sufficie
nt conditions are derived for another controller to be stabilizing and
satisfy the same level of H-infinity performance. Such controllers ar
e said to be (P, gamma)-admissible, where P is the model of the plant
under consideration and gamma is the required level of prespecified H-
infinity, performance. The conditions are expressed as norm bounds on
particular frequency-weighted errors, where the weights are Selected t
o make a specific transfer function a contraction. The design of reduc
ed-order (P,gamma)-admissible controllers is then formulated as a freq
uency-weighted model reduction problem. It is advantageous for the req
uired weights to be large in some sense, Solutions which minimize eith
er the trace, or the determinant, of the inverse weights are character
ized. We show that the procedure for minimizing the determinant of the
inverse weights always gives a direction where the weights are the be
st possible. To conclude, we demonstrate by way of a numerical example
, that when used in conjunction with a combined model reduction/convex
optimization scheme, the proposed design procedures are effective in
substantially reducing controller complexity.