Abstract: The robust H∞ filtering problem is studied using Lyapunov theory. A filter is therefore designed to ensure its robust stability which enables the filtering error to meet the requirements of prescribed H∞ performance for all admissible time-varying uncertainties. An auxiliary system is introduced to simplify the process of deduction, and the sufficient and necessary conditions for the existence of H∞ filter are given. An LMI method for designing filters is obtained through matrixing, thus giving conveniently the expression of filter with LMI as tool kit. A numerical example shows that the method is effective and feasible.