Robust Stabilization of 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 . And so no tuning procedure for scalars and/or matrices is required and the results are less conservative than those of delay - independent. Finally, an illustrative example is presented.