The integral-inequality method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: (x) over dot(t) = Ax(t) + A(1)x(t - h(1) (t)) + B(1)u(t) + B(2)u(t - h(2)(t)). In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a mernoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither (A, B-1) nor (A + A(1), B-1) is stabilizable. (C) 2005 Elsevier Ltd. All rights reserved.