H$\infty$ State Feedback Control for Generalized Continuous/Discrete Time Delay System

In this paper, we consider the problem of designing H$\infty$ state feedback controller for the generalized time systems with delayed states and control inputs in continuous and discrete time cases, respectively. The generalized time delay system problems are solved on the basis of LMI(linear matrix inequality) technique considering time delays. The sufficient condition for the existence of controller and H$\infty$ state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be rewritten as a LMI form in terms of transformed variables. The propose controller design method can be extended into the problem of robust H$\infty$ state feedback controller design method easily.