A simple design method of reduced-order filters and its applications to multirate filter bank design

Based on linear matrix inequality (LMI) technique, a new design method is proposed for the reduced-order filters of continuous and discrete time linear systems. The method is derived from decomposing the key matrix in LMIs which determines the order of designed filters. Different from the existing methods, the proposed method first minimizes the upper bound of the key matrix and then eliminates its near-zero eigenvalues, which results in a simpler, more direct and reliable design procedure. The proposed method can be used to design H2H2 and H∞H∞ reduced-order filters and multirate filter banks. Its effectiveness is illustrated by several examples.