H-infinity control of diffusion systems by using a finite-dimensional controller

In this paper, we consider H-infinity control of linear and semilinear diff usion systems by using a finite-dimensional controller. The main aim is to construct a finite-dimensional stabilizing controller for the linear diffus ion system that makes the H-infinity norm of the closed-loop transfer funct ion less than a given positive number delta. For that purpose, we first der ive a finite-dimensional reduced-order system for the linear diffusion syst em. Then, a stabilizing controller that makes the H-infinity norm of the cl osed-loop transfer function less than another positive number is constructe d for the reduced-order model. It is proved that the finite-dimensional con troller, together with a residual mode filter, plays a role of a finite-dim ensional stabilizing controller that makes the H-infinity norm of the close d-loop transfer function less than delta for the original linear diffusion system if the order of residual mode filter is chosen sufficiently large. M oreover, it is shown that the finite-dimensional H-infinity controller cons tructed for the linear diffusion system also works as a finite-dimensional H-infinity controller for a semilinear diffusion system with sufficiently s mall nonlinear term.