Extended H-infinity Control with Pole Placement Constraints via LMI Approach and Its Application

As well known, extended H-infinity control accepts unstable weighting functions which are included in a generalized plant. On the other hand, the root-clustering problem for H-infinity control has been considered by Chilali and Gahinet and the solution is derived. But the solution can not be applied to extended H-infinity control directly, because the formulation of the root-clustering controllers is discordant with that of extended H-infinity controllers. In this paper, we propose a LMI based design method for this control problem. 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.