Polynomial J-spectral Factorization Research Articles

Polynomial J-spectral factorization method for optimal control of discrete-time systems

We present a simple algorithm for linear-quadratic control of discrete-time systems, based on polynomial J-spectral factorization.

A Toeplitz algorithm for polynomial J-spectral factorization

A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the finite zeros of the input polynomial matrix are given as input data. The algorithm is based on numerically reliable operations only, namely computation of the null-spaces of related block Toeplitz matrices, polynomial matrix factor extraction and linear polynomial matrix equations solving.

A Toeplitz Algorithm for Polynomial J-Spectral Factorization

A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the zeros of the input polynomial matrix are given as input data. Under this assumption, the J-spectral factorization algorithm is based on numerically reliable operations only.

Polynomial J-spectral factorization in minimal state space

By a specific choice of matrices in optimal LQ return difference equality, we develop a simple state-space algorithm for polynomial J-spectral factorization. For this purpose we solve a minimal-order algebraic Riccati equation, the order obtained by solving an Integer Linear Programming (ILP) problem. An example that cannot be solved by the existing algorithms illustrates our algorithm.

A new algorithm for polynomial J-spectral factorization

A new algorithm is illustrated for J-spectral factorization of polynomial matrices. The algorithm is based on the calculus of two-variable polynomial matrices and associated quadratic differential forms, and is especially suited for spectral factorization problems arising in the polynomial and in the behavioral approaches to H∞-control.

New Algorithms for Polynomial J-Spectral Factorization

In this paper new algorithms are developed for J-spectral factorization of polynomial matrices. These algorithms are based on the calculus of two-variable polynomial matrices and associated quadratic differential forms, and share the common feature that the problem is lifted from the original one-variable polynomial context to a two-variable polynomial context. The problem of polynomial J-spectral factorization is thus reduced to a problem of factoring a constant matrix obtained from the coefficient matrices of the polynomial matrix to be factored. In the second part of the paper, we specifically address the problem of computing polynomial J-spectral factors in the context of H∞ control. For this, we propose an algorithm that uses the notion of a Pick matrix associated with a given two-variable polynomial matrix.

On H∞ Problems for 2-D Systems

Robust H∞ control problem for 2-D systems is attacked by polynomial techniques. The design procedure is shown to consist of the same major steps as its 1-D counterpart. For the particular case of the 2-input 2-output considered here this include one scalar polynomial spectral factorization and one matrix polynomial J-spectral factorization. However, the both operation are much more difficult to perform in 2-D.

Polynomial J-spectral factorization

Several algorithms are presented for the J-spectral factorization of a para-Hermitian polynomial matrix. The four algorithms that are discussed are based on diagonalization, successive factor extraction, interpolation, and the solution of an algebraic Riccati equation, respectively. The paper includes a special algorithm for the factorization of unimodular para-Hermitian polynomial matrices and deals with canonical, noncanonical, and nearly noncanonical factorizations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Polynomial solutions toH∞ problems

The paper presents a polynomial solution to the standard H∞-optimal control problem. Based on two polynomial J-spectral factorization problems, a parameterization of all suboptimal compensators is obtained. A bound on the McMillan degree of suboptimal compensators is derived and an algorithm is formulated that may be used to solve polynomial J-spectral factorization problems.