FEEDBACK STABILIZATION OF INFINITE-DIMENSIONAL SYSTEMS WITH PERIODICALLY TIME-VARYING INPUT AND OUTPUT OPERATORS

The stabilization problem of infinite-dimensional systems with periodi cally time-varying bounded input and unbounded output operators is con sidered. The unboundedness of the periodically time-varying ouput oper ators is assumed to be A(gamma)-bounded. For example, the systems cont ain linear diffusion systems with boundary control and observation, wh ere the actuator and sensor influence functions periodically vary with respect to the time variable. The aim of this paper is to show that a controller, which consists of a finite dimensional stabilizing contro ller constructed for the finite-dimensional reduced-order modal model and a residual mode filter, works as a finite-dimensional stabilizing controller for the original infinite-dimensional system if the order o f residual mode filter is chosen to be sufficiently large.