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Ammari, Kais; Tucsnak, Marius

Stabilization of second order evolution equations by a class of unbounded feedbacks. (English) Zbl 0992.93039

ESAIM, Control Optim. Calc. Var. 6, 361-386 (2001).
The system is \[ y''(t) + Ay(t) + Bu(t) = 0, \qquad x(0) = x_0, \quad x'(0) = x_1 \] in Hilbert space, and the aim of this paper is to give conditions that make the closed loop system \((u(t) = BB^*y'(t))\) uniformly stable. The authors give necessary and sufficient conditions for exponential stability and, in the case of nonexponential stability, an explicit decay rate for initial data in certain subspaces.
Reviewer: Hector O.Fattorini (Los Angeles)

Cited in 9 Reviews
Cited in 91 Documents

MSC:

93C25 Control/observation systems in abstract spaces
93D15 Stabilization of systems by feedback
93B07 Observability

Keywords:

stabilization by feedback; infinite dimensional systems; controllability; observability; exponential stability; decay rate
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Full Text: DOI Numdam EuDML

References:

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