Frequency-selective KYP lemma, IIR filter, and filter bank design

Abstract

For a transfer function F(ejω) of order n, Kalman-Yakubovich-Popov (KYP) lemma characterizes a general intractable semi-infinite programming (SIP) condition by a tractable semidefinite programming (SDP) for the entire frequency range. Some recent results generalize this lemma for a certain frequency interval. All these SDP characterizations are given at the expense of the introduced Lyapunov matrix variable of dimension n × n. Consequently, formulation and design of high dimensional problem is challenging. Moreover, existing SDP characterizations for frequency-selective SIP (FS-SIP) do not allow to formulate synthesis problems as SDPs. In this paper, we propose a completely new SDP characterization of general FS-SIP involving SDPs of moderate size and free from Lyapunov variables. Furthermore, a systematic IIR filter and filter bank design is developed in a similar vein, with several simulations provided to validate the effectiveness of our SDP formulation. © 2009 IEEE