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ON CONDITIONS FOR ASYMPTOTIC STABILITY OF DISSIPATIVE INFINITEDIMENSIONAL SYSTEMS WITH INTERMITTENT DAMPING
, 2012
"... Abstract. We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is infinitedimensional then the system needs not being asymptotical ..."
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Abstract. We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is infinitedimensional then the system needs not being asymptotically stable (not even in the weak sense). Exponential stability is recovered under a generalized observability inequality, allowing for timedomains that are not intervals. Weak asymptotic stability is obtained under a similarly generalized unique continuation principle. Finally, strong asymptotic stability is proved for intermittences that do not necessarily satisfy some persistent excitation condition, evaluating their total contribution to the decay of the trajectories of the damped system. Our results are discussed using the example of the wave equation, Schrödinger’s equation and, for strong stability, also the special case of finitedimensional systems.
Stabilization of twodimensional persistently excited linear control systems with arbitrary rate of convergence
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pp. X–XX STARS OF VIBRATING STRINGS: SWITCHING BOUNDARY FEEDBACK STABILIZATION
, 2011
"... (Communicated by the associate editor name) Abstract. We consider a starshaped network consisting of a single node with N ≥ 3 connected arcs. The dynamics on each arc is governed by the wave equation. The arcs are coupled at the node and each arc is controlled at the other end. Without assumptions ..."
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(Communicated by the associate editor name) Abstract. We consider a starshaped network consisting of a single node with N ≥ 3 connected arcs. The dynamics on each arc is governed by the wave equation. The arcs are coupled at the node and each arc is controlled at the other end. Without assumptions on the lengths of the arcs, we show that if the feedback control is active at all exterior ends, the system velocity vanishes in finite time. In order to achieve exponential decay to zero of the system velocity, it is not necessary that the system is controlled at all N exterior ends, but stabilization is still possible if, from time to time, one of the feedback controllers breaks down. We give sufficient conditions that guarantee that such a switching feedback stabilization where not all controls are necessarily active at each time is successful.
2 ON CONDITIONS FOR ASYMPTOTIC STABILITY OF DISSIPATIVE INFINITEDIMENSIONAL SYSTEMS WITH INTERMITTENT DAMPING
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ProjectTeam GECO
"... Optimization and control of dynamic systems Table of contents ..."
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