Finite-Dimensional H Control of a Class of ` Infinite-Dimensional Linear Time-Varying Systems*

In this paper, we consider H control of infinite-dimensional linear time-varying ` IDLTV.systems whose homogeneous parts are of modal type, by using a finitedimensional controller. The aim is to construct a finite-dimensional stabilizing controller for the IDLTV system that makes the norm of the closed-loop operator less than a given positive number d . To this end, a finite-dimensional model is firstly derived for the IDLTV system, and a stabilizing controller that makes the norm of the closed-loop operator less than another positive number g -d.is constructed for the finite-dimensional model. Then it is shown that a controller, which consists of a residual mode filter and the controller mentioned above, becomes a finite-dimensional stabilizing controller for the given IDLTV system such that the closed-loop operator has norm less than d , if the order of the residual mode filter is chosen sufficiently large.