LMI approach in stability and control of time-delay systems

In this paper, stability and stabilization conditions in the form of linear matrix inequalities and control of linear time-delay systems are discussed. A lot of stability conditions are reported, but there are few conditions which can derive LMI conditions on various control problems. We show three different stability and stabilizability criteria, that is delay independent criteria which are independent on the length of the delay, delay dependent criteria and a new less conservative criterion which is using an auxiliary system.