In this paper, we investigate the effect of time delays in boundary or internal feedback stabilization of the Schrödinger equation. In both cases, under suitable assumptions, we establish sufficient conditions on the delay term that guarantee the exponential stability of the solution. These results are obtained by using suitable energy functionals and some observability estimates.
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Serge Nicaise, Salah-eddine Rebiai, Stabilization of the Schrödinger equation with a delay term in boundary feedback or internal feedback. Port. Math. 68 (2011), no. 1, pp. 19–39DOI 10.4171/PM/1879