Finite Frequency H

This paper investigates the problem of finite frequency (FF) H∞ filtering for time-delayed singularly perturbed systems. Our attention is focused on designing filters guaranteeing asymptotic stability and FF H∞ disturbance attenuation level of the filtering error system. By the generalized Kalman-Yakubovich-Popov (KYP) lemma, the existence conditions of FF H∞ filters are obtained in terms of solving an optimization problem, which is delay-independent. The main contribution of this paper is that systematic methods are proposed for designing H∞ filters for delayed singularly perturbed systems

Characterizations of rectangular (para)-unitary rational Functions

We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle: (i) Through the realization matrix of Schur stable systems. (ii) The Blaschke-Potapov product, which is then employed to introduce an easy-to-use description of all these functions with dimensions and McMillan degree as parameters. (iii) Through the (not necessarily reducible) Matrix Fraction Description (MFD). In cases (ii) and (iii) the poles of the rational functions involved may be anywhere in the complex plane, but the unit circle (including both zero and infinity). A special attention is devoted to exploring the gap between the square and rectangular cases.Comment: Improved versio

Characterizations of Families of Rectangular, Finite Impulse Response, Para-Unitary Systems

We here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class U). First, we offer three characterizations of these systems. Then, introduce a description of all FIRs in U, as copies of a real polytope, parametrized by the dimensions and the McMillan degree of the FIRs. Finally, we present six simple ways (along with their combinations) to construct, from any FIR, a large family of FIRs, of various dimensions and McMillan degrees, so that whenever the original system is in U, so is the whole family. A key role is played by Hankel matrices

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

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

Frequency selective KYP lemma and its applications to IIR filter bank design

For a transfer function/filter F(εω) of order n, Kalman-Yakubovich-Popov (KYP) lemma characterizes the intractable semi-infinite programming (SIP) condition F(εω)1 ⊖(ε ω)T ≥ 0 V ω in frequency domain by a tractable semi-definite programming (SDP) in state-space domain. Some recent results generalize this lemma to SDP for SIP of frequency selectivity(FS-SIP). All these SDP characterizations are given at the expense of the introduced Lyapunov matrix variable of dimension n × n, making them impractical for high order problem. Moreover, the existing SDP characterizations for FS-SIP do not allow to formulate synthesis/design problems as SDPs. In this paper, we propose a completely new SDP characterization of general FS-SIP, which is of moderate size and is free from Lyapunov variables. Extensive examples are provided to validate the effectiveness of our result. © 2007 IEEE