The problem of robust $H_{infty}$ estimation for the polytopic uncertain linear system with state delay is considered. Firstly, by introducing two auxiliary matrices a new LMI representation of $H_{infty}$ performance is presented for the linear systems with a single time-varying state delay. The proposed criterion exhibits a kind of separation between the system 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.