This paper proposes a method for robust reduced-order $H_{infty}$ filter design for poly topic uncertain systems, using linear matrix inequalities (LMIs). Sufficient LMI conditions for both robust full- and reduced-order $H_{infty}$, filter design are derived. Convex optimization problems are formulated and solved to obtain optimal $H_{infty}$ filters by using the resulting LMI conditions. The resulting conditions do not involve any non-convex rank constraints, and thus the proposed method for $H_{infty}$ filter design guarantees global optimum solutions. Numerical examples are presented to show the effectiveness of the proposed method.