Volume 9 (2026)
Nguyen, Hoai-Minh
Rapid stabilization and finite time stabilization of the bilinear Schrödinger equation
Annales Henri Lebesgue, Volume 9 (2026), pp. 929-975

Metadata

DOI10.5802/ahl.279
Keywords rapid stabilization ,  finite-time stabilization ,  Schrödinger equation ,  Gramian operator ,  optimal control ,  Riccati equation

Abstract

We propose a method to establish the rapid stabilization of the bilinear Schrödinger control system and its linearized system, and the finite-time stabilization of the linearized system using the Grammian operators. The analysis of the rapid stabilization involves a new quantity (variable) which is inspired by the adjoint state in the optimal control theory and is proposed in our recent work on control systems associated with strongly continuous group, and a new regularizing effect of the control system. The analysis of the finite-time stabilization follows the strategy introduced by Coron and Nguyen in the study of the finite-time stabilization of the heat equation and incorporates a new ingredient involving the estimate of the cost of controls of the linearized system in small time derived in this paper.


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