Rapport complet stabilité et stabilisation des systèmes linéaires à paramétrés distribues avec retards, tutoriel & document PDF.

The problem of stability for systems governed by partial dierential equations (coupled wave  quations, coupled Euler-Bernoulli equations, transmission wave equations) with delay terms in the boundary or internal feedback is considered. Under some assumptions exponential stability is established. The results are obtained by introducing an appropriate energy function and by proving a suitable observability inequality.

Shang et al [38] investigated the stability of one dimensional Euler Bernoulli beam with input delay in the boundary control by using spectral analysis and Lyapunov method.
The purpose of this thesis is to study the stability and stabilization of some distributed parameter systems with time delays. We begin with compactly coupled wave equations with delay terms in the boundary or internal feedbacks. In the second chapter, the system of transmission of the wave equation with a delay term in the boundary feedback is considered, whereas chapter three treats the transmission wave equation where both boundary and internal feedbacks contain a delay term. Coupled Euler-Bernoulli equations with delay terms in the boundary feedback controller are studied in chapter four. Finally chapter ve is devoted to coupled Euler-Bernoulli equations with distributed controllers containing a delay term. Under some assumptions exponential stability is established.
The results are obtained by introducing an appropriate energy function and by proving a suitable observability estimate.

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