A new proportional-integral (PI) sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller (ASMC) is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the Hoo control problem by designing a memoryless Hoo state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level y in an iioo sense. The admissible state feedback controller can be found by solving

a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method This design scheme combines the strong robustness of the sliding mode control with the Hoo norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.

sliding mode control, Hoo control, nonlinearity, state-delayed system, linear matrix inequality (LMIs)