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The issues of stability and H∞ control of linear systems with time-varying delays are considered. Based on the Lyapunov-Krasovskii approach and on Finsler's projection lemma, delay-dependent sufficient conditions are obtained, in terms of linear matrix inequalities (LMIs), for the stability of these systems. These conditions generalize previous results that were derived using either the descriptor approach or the first and the third model transformations. The obtained criteria are extended to deal with: stabilizability, the bounded real lemma and the H∞ state-feedback control.