Finite-dimensional H∞ control of a class of infinite-dimensional linear time-varying systems

rn this paper, we consider H-infinity control of infinite-dimensional linear time-varying (IDLTV) systems whose homogeneous parts are of modal type, by using a finite-dimensional 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 delta. 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 gamma(<delta) 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 delta, if the order of the residual mode filter is chosen sufficiently large. (C) 1997 Academic Press.