We construct a specific feedback control scheme for a class of linear parabolic systems such that some nontrivial linear functionals of the state decay faster than the state, while the state is stabilized. In particular, we raise a new question of pole allocation which is subject to constraint, and derive the necessary and sufficient condition: an essential extension of the well known result by W. M. Wonham (1967).
"Stabilization and decay of functionals for linear parabolic control systems." Proc. Japan Acad. Ser. A Math. Sci. 84 (2) 19 - 24, February 2008. https://doi.org/10.3792/pjaa.84.19