A linear matrix inequality approach for robust control of systems with delayed states

This paper addresses the robust stabilization problem for uncertain systems with delayed states. The parameter uncertainties are unknown but norm-bounded and the delay is time-varying. In this study, a linear matrix ineaquality approach for robust stability analysis for the nominal unforced system and a method for robust stabilization for a class of uncertain delay systems via linear memoryless state feedback control are presented. The results depend on the size of the delay and are given in terms of linear matrix inequalities.