Delay-dependent stability and H ∞ control: Constant and time-varying delays

Abstract

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, we compare methods under different transformations and show the advantages of the descriptor one. We obtain new delay-dependent stability conditions for systems with time-varying delays 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.