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Stabilization of the wave equation by optimal control: Estimate of the decay rate. (Stabilisation de l’équation des ondes par un contrôle optimal distribué: Estimation du taux de décroissance.) (French. Abridged English version) Zbl 0809.93027
Summary: Considering an optimal control problem with infinite horizon associated to the wave equation, it is known that the energy decreases exponentially. We derive an estimation of the factor of decay which is expressed as a function of the norm of the Riccati operator.

93C20 Control/observation systems governed by partial differential equations
35L05 Wave equation
49J20 Existence theories for optimal control problems involving partial differential equations
93D20 Asymptotic stability in control theory