Abdelaziz Rhandi

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We show that the class of regular time varying systems is invariant under perturbations by time–varying state and input delays. In particular, we give explicit formulas of the resulting input, output, and input–output maps. This result is used to solve the feedback problem for the delayed system. The relationship between the open and the closed loop system(More)
We consider time dependent perturbations B(t) of a non{autonomous Cauchy problem _ v(t) = A(t)v(t) (CP) on a Banach space X. The existence of a mild solution u of the perturbed problem is proved under Miyadera type conditions on B(). In the parabolic case and X = L d ((), 1 < d < 1, we show that u is diierentiable a.e. and satisses _ u(t) = (A(t)+B(t))u(t)(More)
We prove that the spectrum of the innnite-dimensional Laplacian is the left half plane f 2 C : Re 0g. As a consequence, we obtain a simple proof of the norm discontinuity of the generated semigroup. Let H be a separable, innnite dimensional, real Hilbert space and let (e k) be an or-thonormal basis. We denote by BUC(H) the space of all bounded, uniformly(More)
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