ℒ2- gain control of time-delay systems with actuator saturation

Disturbance attenuation problem in terms of ℒ_2-gain for continuous linear time-delay (LTD) systems with nonzero initial conditions, time-varying delays and saturating control is addressed where the disturbances acting on the system are with bounded energy. First, a group of sufficient conditions in terms of bilinear matrix inequalities (BMIs) are obtained. Then, to solve this problem, cone complementary linearization method is adopted to the problem. The proposed method utilizes convex description of nonlinear saturation phenomenon by means of convex hull of some linear feedback which leads to a few additional ellipsoidal conditions in terms of linear matrix inequalities (LMIs). The validity of the method is illustrated through some examples at the end.