This note addresses the design of robust W2 filters for linear systems with a state-space model subject to time-varying uncertain parameters with limited variation. The uncertain parameters and their rate of variation are assumed to belong to a given convex-bounded polyhedral domain. A method based on a parameter-dependent Lyapunov function is proposed for designing a linear stationary asymptotically stable filter with a guaranteed average error variance, irrespective of the uncertain parameters. The proposed design is formulated in terms of linear matrix inequalities.