This paper introduces a new approach to H2 robust filtering design for discrete LTI systems subjected to linear fractional parameter uncertainty representation. We calculate a performance certificate in terms of the gap between the lower and the upper bounds of a minimax programming problem, which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load. © 2008 IEEE. 19021907Anderson, B.D.O., Moore, J.B., (1979) Optimal Filtering, , Englewood Cliffs, New JerseyBoyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaGeromel, J.C., de Oliveira, M.C., Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions (2002) SIAM J. Optim. Contr, 41 (3), pp. 700-711Geromel, J.C., Korogui, R.H., H2 robust filter design with performance certificate via convex programming (2008) Automatica, 44 (4), pp. 937-948Geromel, J.C., Regis Filho, L.A.V., H2 optimal robust filtering (2006) European Journal of Control, 12 (1), pp. 30-39Hoang, N.T., Tuan, H.D., Apkarian, P., Hosoe, S., Robust filtering for discrete nonlinear fractional transformation systems (2004) IEEE Trans. Circ. Syst.-II, 51 (11), pp. 587-592. , NovemberIwasaki, T., Hara, S., Well-posedness of feedback systems: Insights into exact robustness analysis and approximate computations (1998) IEEE Trans. on Automat. Contr, 43 (5), pp. 619-630. , MayKorogui, R.H., Geromel, J.C., Robust H2 Filtering for Continuous Time Systems with Linear Fractional Representation (2008) Proceedings of the 17th IFAC World Congress, pp. 2675-2680. , Seoul, Korea, JulyMatick, R.E., (1969) Transmission Lines for Digital and Communication Networks, , McGraw-HillRockafellar, R., (1970) Convex Analysis, , Princeton PressScherer, C.W., Köse, I.E., Robust H2 estimation with dynamic IQCs: A convex solution (2006) Proceedings of the 45th IEEE CDC, pp. 4746-4751. , San Diego, CA, DecemberShaked, U., Xie, L., Soh, Y.C., New approachs to robust minimum variance filter design (2001) IEEE Trans. Signal Proces, 49 (11). , 2620-2629, NovemberTheodor, Y., Shaked, U., Robust discrete-time minimum variance filtering (1996) IEEE Trans. Signal Proces, 44, pp. 181-189