Abstract :
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.
