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In this paper we consider the wave equation on 1-d networks with a delay term in the boundary and/or transmission conditions. We first show the well posedness of the problem and the decay of an appropriate energy. We give a necessary and sufficient condition that guarantees the decay to zero of the energy. We further give sufficient conditions that lead to… (More)

We consider abstract second order evolution equations with unbounded feedback with time-varying delay. Existence results are obtained under some realistic assumptions. We prove the exponential decay under some conditions by introducing an abstract Lyapunov functional. Our abstract framework is applied to the wave, to the beam and to the plate equations with… (More)

In this paper we study the stabilization of the wave equation on general 1-d networks. For that, we transfer known observability results in the context of control of conservative systems (see [14]) into a weighted observability estimate for the dissipative one. Then we use an interpolation inequality similar to the one proved in [7] to obtain the explicit… (More)

We consider an infinite dimensional system modeling a boost converter connected to a load via a transmission line. The governing equations form a system coupling the telegraph partial differential equation with the ordinary differential equations model-ing the converter. The coupling is given by the boundary conditions and the nonlinear controller we… (More)

— We consider a class of infinite dimensional systems involving a control function u taking values in [0, 1]. This class contains, in particular, the average models of some infinite dimensional switched systems. We prove that the system is well-posed and obtain some regularity properties. Moreover, when u is given in an appropriate feedback form and the… (More)

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