Feedback control of semilinear diffusion systems: inertial manifolds for closed-loop systems

An approach via inertial-manifold theory is presented as a wayto study the problem of stabilizing semilinear diffusion systemsusing finite-dimensional controllers. It is shown that a Sakawatype of controller plays an important role in the constructionof an inertial manifold for the closed-loop (controlled) semilineardiffusion system. This means that the use of a Sakawa type ofcontroller reduces the stabilization problem for the closed-loopsystem to the one on the inertial manifold. ^*This paper was partially presented at the 12th IFAC World Congress,Sydney, 18–23 July 1993.