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The problem of compensation analysis for networked control systems with uncertain network-induced delay and norm bounded unknown input is investigated. By introducing two slack matrices, an improved sufficient condition for the existence of stabilized state feedback controller is presented, which is dependent on the minimum and maximum delay bounds. And the controller design approach is proposed in the letter. The newly proposed criterion exhibits a kind of separation between the systems matrices and the positive definite Lyapunov matrices. So the vertex-dependent Lyapunov functions can be adopted, and thus a less conservative result is expected to be obtained. A numerical example is employed to illustrate the effect of the proposed approach.