H-infinity-output feedback of infinite-dimensional systems via approximation

As in the finite-dimensional case, a state-space based controller for the i nfinite-dimensional H-infinity disturbance-attenuation problem may be calcu lated by solving two Riccati equations. These operator Riccati equations ca n rarely be solved exactly. We approximate the original infinite-dimensiona l system by a sequence of finite-dimensional systems. The solutions to the corresponding finite-dimensional Riccati equations are shown to converge to the solution of the infinite-dimensional Riccati equations, Furthermore, t he corresponding finite-dimensional controllers yield performance arbitrari ly close to that obtained with the infinite-dimensional controller. (C) 200 1 Elsevier Science B.V. All rights reserved.