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As well known, extended H∞ control accepts unstable weighting functions which are included in a generalized plant, so it has wider availability than standard H∞ control. On the other hand, the root-clustering problem for H∞ control has been considered by Chilali and Gahinet and the solution is derived. But it is not so easy to apply the solution to extended H∞ control, because the formulation of the root-clustering controllers is discordant with that of extended H∞ controllers. Therefore, we can not simply combine the root-clustering conditions with extended H∞ control. In this paper, we propose a LMI based design method for this control problem by using modified formulation of controllers of the rootclustering problem derived by Chilali and Gahinet. These types of control problems appear in design problems of a vibration isolation controller which attenuates vibrations forced by narrow-band frequency disturbances. A controller for a simple vibration isolation experimental system is designed by the proposed method and performance of a designed controller is verified by experimental results. Copyright c ©2005 IFAC.

Extended H^|^infin; Control with Pole Placement Constraints via LMI Approach and Its Application