Robust controller designing for delayed systems with rank-1 type uncertainties

This paper deals with the problem of robust stabilization for the systems with rank-1 type uncertainties and multiple state delay. Firstly, a new delay-dependent criteria is presented for unforced normal delayed system to be stable. Based on the obtained criteria, a new LMI approach is developed for robust stabilization of a class of uncertain delay systems via linear memoryless state feedback control law. The results depend on the size of the delays and are given in terms of linear matrix inequalities. No tuning procedure for scalars and/or matrices is required and the results are less conservative than those of delay-independent systems. Finally, an illustrative example is presented