A projection approach to H∞ control of time-delay systems

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. In addition to the new perspective it gives to the problems of control of systems with time-delay, the new approach provides new degrees of freedom in the design stage. These degrees of freedom lead to results that are less conservative than those obtained by the descriptor approach for systems with parameter uncertainties.