Rapid stabilization of parabolic coupled system

Abstract

This paper considers the problem of stabilizing a class of non-scalar coupled parabolic equations controlled by a single multiplicative control. We show that if the associated linear system is null controllable, then the solution of the considered system can be locally superexponentially stabilized towards specific trajectories, referred to as eigen-trajectories. To resolve the null controllability issue, we reformulate it as a moment problem and apply two separate sets of assumptions on the eigenvalues. Some applications are presented to illustrate the obtained results.