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The design problem of a delay-dependent robust H∞ controller for uncertain descriptor systems with time-varying discrete and distributed delays is investigated. The designed controller can guarantee the closed-loop system is regular, impulse-free and exponentially stable with an H∞ norm bound constraint. The obtained criteria to derive an efficient robust H∞ control design are expressed as a set of nonconvex matrix inequalities, which can be solved by combining both the linear matrix inequalities technique and the cone complementarity method. Two numerical examples are given to demonstrate effectiveness and less conservativeness of the proposed method.