Abstract: This paper considers the H∞ stabilization problems for plants with both state delay and control delay. Based on dissipative dynamical system theory and differential game principle, a quadratic storage function with integral items which include the past memory information during the delay span is employed to design H∞ state feedback controller and observer-based H∞ output feedback controller. These two problems are converted to mathematical problems of solving some matrix inequalities and Riccati equations which are dependent on the time delays. Besides, the controller laws can make the closed systems intenally stable and guarantee disturbance attenuation.