Under spectral assumptions, a Riccati feedback from a POD finite-dimensional approximation exponentially stabilizes the infinite-dimensional linear control system.
Zabczyk, Mathematical control theory, An introduction, Reprint of the 1995 edition, Mod- ern Birkh¨ auser Classics
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Stabilization of infinite-dimensional linear control systems by POD reduced-order Riccati feedback
Under spectral assumptions, a Riccati feedback from a POD finite-dimensional approximation exponentially stabilizes the infinite-dimensional linear control system.