The polar decomposition of block companion matrices

AbstractLet L(λ) = Inλm + Am−1λm−1 + …+A1λ + A0 be an n × n monic matrix polynomial, and let CL be the corresponding block companion matrix. In this note, we extend a known result on scalar polynomials to obtain a formula for the polar decomposition of CL when the matrices A0 and Σj=1m−1 AjA*j are nonsingular

A note on the controllability of higher-order linear systems

In this paper, a new condition for the controllability of higher-order linear dynamical systems is obtained. The suggested test contains rank conditions of suitably defined matrices and is based on the notion of compound matrices and the Binet-Cauchy formula. © 2004 Elsevier Ltd. All rights reserved

A note on the controllability of higher order linear systems

In this paper, a new condition for the controllability of higher order linear dynamical systems is obtained. The suggested test contains rank conditions of suitably defined matrices and is based on the notion of compound matrices and the Binet-Cauchy formula. Key words: companion matrix, compound matrix, closed loop system, eigenvalue, input vector, matrix polynomial, stat

A note on the controllability of higher-order linear systems

In this paper, a new condition for the controllability of higher-order linear dynamical systems is obtained. The suggested test contains rank conditions of suitably defined matrices and is based on the notion of compound matrices and the Binet-Cauchy formula. (C) 2004 Elsevier Ltd. All rights reserved

Some extensions of the residual lifetime and its connection to the cumulative residual entropy

In this article we present a sequence of random variables with weighted tail distribution functions, constructed based on the relevation transform. For this sequence, we prove several recursive formulas and connections to the residual entropy through the unifying framework of the Dickson–Hipp operator. We also give some numerical examples to evaluate our results

The polar decomposition of block companion matrices

Let L(λ) = Inλm + A m-1λm-1 + ...+A1λ + A0 be an n × n monic matrix polynomial, and let CL be the corresponding block companion matrix. In this note, we extend a known result on scalar polynomials to obtain a formula for the polar decomposition of C L when the matrices A0 and Σj=1 m-1 AjA*j are nonsingular. © 2005 Elsevier Ltd. All rights reserved

Some extensions of the residual lifetime and its connection to the cumulative residual entropy

In this article we present a sequence of random variables with weighted tail distribution functions, constructed based on the relevation transform. For this sequence, we prove several recursive formulas and connections to the residual entropy through the unifying framework of the Dickson–Hipp operator. We also give some numerical examples to evaluate our results

On the computation of the Jordan canonical form of regular matrix polynomials

AbstractIn this paper, an algorithm for the computation of the Jordan canonical form of regular matrix polynomials is proposed. The new method contains rank conditions of suitably defined block Toeplitz matrices and it does not require the computation of the Jordan chains or the Smith form. The Segré and Weyr characteristics are also considered