Robust analysis and synthesis for delayed systems with rank-1 type uncertainties

This paper deals with the problem of robust stability analysis and synthesis for systems with rank-1 type uncertainties and multiple state delays. A new delay-dependent criterion is presented for the stability of unforced nominal delayed systems. Based on the obtained criterion, a new linear matrix inequality (LMI) approach is developed for the robust stabilization of a class of uncertain delayed systems via a linear memoryless state feedback control law. The results are dependent on the size of the delays and are given in terms of LMIs. The presented method does not require a tuning procedure for scalars and/or matrices and produces results that are less conservative than delay-independent results. Finally, two illustrative examples are presented