Three main model transformations were used in the past for delay-dependent stability. Recently a new (descriptor) model transformation has been introduced. In the present paper for systems with time-varying delays we obtain new delay-dependent stability conditions under descriptor model transformation. These conditions are written in terms of linear matrix inequalities. We also refine recent results on delay-dependent H_∞ control and extend them to the case of time-varying delays. Numerical examples illustrate the effectiveness of our method.