Frederick W. Fairman

QR-factorization method for computing the greatest common divisor of polynomials with inexact coefficients

This paper presents a novel means of computing the greatest common divisor (GCD) of two polynomials with real-valued coefficients that have been perturbed by noise. The method involves the QR-factorization of a near-to-Toeplitz matrix derived from the Sylvester matrix of the two polynomials. It turns out that the GCD to within a constant factor is contained in the last nonzero row of the upper triangular matrix R in the QR-factorization of the near-to-Toeplitz matrix. The QR-factorization is efficiently performed by an algorithm due to Chun et al. (1987). A condition number estimator due to Bischof (1990) and an algorithm for rank estimation due to Zarowski (1998) are employed to account for the effects of noise.

Design of multifunctional reduced order observers

Abstract This paper presents a method for the design of an observer capable of reconstucting several linear functionals of the states of a linear, finite-dimensional system. The goal of this method is the design of an observer having minimum order subject to the restriction that the observer eigenvalues be freely assignable. The method is based on the reduction of a state observer formulated from an observable canonic form for the system when the functionals are treated as if they were additional outputs.

Parameter identification for a class of distributed systems

A new practical method, hereby called the ‘moment functional method’, is presented for the identification of the parameters of distributed parameter systems characterized by either the one-dimensional wave or diffusion equation. The method is extended to include systems characterized by a one-dimensional diffusion equation with a coefficient which is a polynomial in time. In this case the method determines the coefficients in the polynomial. The feasibility of the method lies in the on-line generation of linear time-invariant algebraic equations in the unknown system parameters by means of two Poisson filter chains which are fed from three points along the distributed system. The results of simulation studies are presented to illustrate the applicability of the method.

Balanced realization of orthogonally symmetric transfer function matrices

Structural properties of minimal balanced realizations of orthogonally symmetric transfer function matrices are developed. These properties are then used to formulate a computationally efficient algorithm for determining balanced realizations of transfer function matrices in this class. The applicability of these realizations to circuit synthesis is indicated.

Separately balanced realization and model reduction of 2-D separable-denominator transfer functions from input - output data

A method which uses 2-D pulse response data is developed for the determination of a separately balanced state-space model of a quarter-plane, causal, recursive, separable-denominator (CRSD) transfer function. This algorithm involves the Cholesky decomposition of two matrices constructed directly from the given data and the determination of the eigenvalues and eigenvectors of two real symmetric matrices which are determined directly from the given data and the matrices determined from the Cholesky decomposition.

Harmonic retrieval via state space and fourth-order cumulants

The harmonic retrieval problem considered concerns the estimation of the frequencies in a sum of complex sinusoids in the presence of Gaussian measurement noise. The method developed for solving this problem relies on the use of a diagonal form state space model representation of the harmonic retrieval problem. Fourth-order cumulants are employed as the signal processing technique. It is shown that using this approach the unknown frequencies can be estimated by finding the eigenvalues of a symmetric matrix made up from the cumulants of the data. Simulation results show the effectiveness of this method when the signals are corrupted by Gaussian noise (white or colored). >

Stabilization of 2D filters using 2D observers

The extension of Luenbergers observer theory to 2D systems is considered. Equations are developed for the design of 2D observers Conditions are given for the use of these observers in the stabilization of 2D systems through state feedback.

Factorable FIR Nyquist filters with least stopband energy under sidelobe level constraints

Spectrally factorable Nyquist filters are used in data communications to avoid intersymbol interference. An approach is developed for obtaining a Nyquist filter that is factorable having the smallest stopband energy for a given sidelobe level. The resulting constrained minimization problem is solved efficiently and reliably using the Goldfarb-Idnani (1983) algorithm. Some examples are presented comparing the present method with a previous approach from the literature.

A note on cross Grammians for orthogonally symmetric realizations

The orthogonally symmetric property of realizations of orthogonally symmetric transfer function matrices is used to extend the result reported in [4]-[6] concerning cross Grammians of multiinput-multioutput systems. Two numerical examples are given to illustrate the generalization proposed here.

Robust stabilization of nonlinear plants—anL2 approach

This paper extends the theory of H∞ control for linear plants to input affine nonlinear plants without special output structure. This result is used to develop solutions to the robust stabilization problem for several classes of uncertain nonlinear plants.