Exponential Stability of Compactly Coupled Wave Equations with Delay Terms in the Boundary Feedbacks

Abstract : We consider a linear system of compactly coupled wave equations with Neumann feedback controllers that contain delay terms. First, we prove under some assumptions that the closed-loop system generates a $$C_{0}-$$semigroup of contractions on an appropriate Hilbert space. Then, under further assumptions, we show that the closed-loop system is exponentially stable. This result is obtained by introducing a suitable energy function and by using an observability estimate.
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Salah-Eddine Rebiai, Fatima Sidi Ali. Exponential Stability of Compactly Coupled Wave Equations with Delay Terms in the Boundary Feedbacks. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. pp.278-284, ⟨10.1007/978-3-662-45504-3_27⟩. ⟨hal-01286436⟩

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