On Computing J Inner Outer Factorizations of Rational Matrices
نویسندگان
چکیده
In this paper we propose a new numerically reliable computational approach to determine the J inner outer factorization of a rational matrix G The proposed approach is completely general being ap plicable whenever G is proper or not or of full column row rank or not In contrast to existing one shot methods which require the solution of Riccati or generalized Riccati equations the new approach is recursive and avoids such computatio nally involved steps by using instead a recursive state space approach The resulting factors have always minimal order descriptor representations
منابع مشابه
A note on computing range space bases of rational matrices
We discuss computational procedures based on descriptor state-space realizations to compute proper range space bases of rational matrices. The main computation is the orthogonal reduction of the system matrix pencil to a special Kronecker-like form, which allows to extract a full column rank factor, whose columns form a proper rational basis of the range space. The computation of several types ...
متن کاملRational and Polynomial Matrices
where λ = s or λ = z for a continuousor discrete-time realization, respectively. It is widely accepted that most numerical operations on rational or polynomial matrices are best done by manipulating the matrices of the corresponding descriptor system representations. Many operations on standard matrices (such as finding the rank, determinant, inverse or generalized inverses, nullspace) or the s...
متن کاملGeneralized Schur Methods to Compute Coprime Factorizations of Rational Matrices
Numerically reliable state space algorithms are proposed for computing the following stable coprime factorizations of rational matrices factorizations with least order denominators factorizations with inner denominators and factorizations with proper stable factors The new algorithms are based on a recursive generalized Schur algorithm for pole assignment They are generally applicable regardles...
متن کاملComputation of general inner-outer and spectral factorizations
In this paper we solve two problems in linear systems theory: the computation of the inner–outer and spectral factorizations of a continuous–time system considered in the most general setting. We show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic Riccati equation of order usually much smaller than the McMillan degree of the trans...
متن کاملComputation of Inner-Outer Factorizations of Rational Matrices
In this paper we propose a new numerically reliable computational approach to determine the inner-outer factorization of a rational transfer matrix G of a linear descriptor system. In contrast to existing computationally involved “one-shot” methods which require the solution of Riccati or generalized Riccati equations, the new approach relies on an efficient recursive zeros dislocation techniqu...
متن کامل