Cristian Oara

Computation 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 transfer function matrix of the system. The proposed procedures are completely general, being applicable for a polynomial/proper/improper system whose transfer function matrix could be rank deficient and could have poles/zeros on the imaginary axis or at infinity. As an application we discuss the extension to the case of rational matrices of the complete orthogonal decomposition of a constant matrix. Numerical refinements and examples illustrating the proposed approach, are discussed in detail.

Minimal Degree Coprime Factorization of Rational Matrices

Given a rational matrix G with complex coefficients and a domain

Spectral and inner-outer factorizations for discrete-time systems

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Optimal Distributed Control for Platooning via Sparse Coprime Factorizations

in the closed complex plane, both arbitrary, we develop a complete theory of coprime factorizations of G over

Solutions to the general inner-outer and spectral factorization problems

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Structured coprime factorizations description of Linear and Time-Invariant networks

, with denominators of McMillan degree as small as possible. The main tool is a general pole displacement theorem which gives conditions for an invertible rational matrix to dislocate by multiplication a part of the poles of G. We apply this result to obtain the parametrized class of all coprime factorizations over

Squaring-Down Descriptor Systems: Constructive Solutions and Numerical Algorithms

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On computing normalized-coprime factorizations of general rational matrices

with denominators of minimal McMillan degree nb---the number of poles of G outside

Least order coprime factorizations of rational matrices: the canonical case

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Singular Riccati theory via extended symplectic pencils

. Specific choices of the parameters and of