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IMA Journal of Mathematical Control and Information 1994 11(1):75-92; doi:10.1093/imamci/11.1.75
© 1994 by Institute of Mathematics and its Applications
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Feedback control of semilinear diffusion systems: inertial manifolds for closed-loop systems*

HIDEKI SANO and NOBORU KUNIMATSU

Department of Electrical Engineering, Keio University 3-14-1 Hiyoshi, Kohoku, Yokohama 223, Japan
Department of Mathematics, Keio University 3-14-1 Hiyoshi, Kohoku, Yokohama 223, Japan

An approach via inertial-manifold theory is presented as a way to study the problem of stabilizing semilinear diffusion systems using finite-dimensional controllers. It is shown that a Sakawa type of controller plays an important role in the construction of an inertial manifold for the closed-loop (controlled) semilinear diffusion system. This means that the use of a Sakawa type of controller reduces the stabilization problem for the closed-loop system to the one on the inertial manifold.

*This paper was partially presented at the 12th IFAC World Congress, Sydney, 18–23 July 1993.


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