论文信息 - On Solvents of Matrix Polynomials

On Solvents of Matrix Polynomials

This paper is concerned with the construction of right and left solvents (also called block roots) of a matrix polynomial from latent roots and vectors. It addresses also the important case of the existence of a complete set of block roots. Solvents do not always exist, so conditions for the existence of such solvents are discussed. The inverse of a matrix polynomial is obtained as a particular case of the block partial fraction expansion of a related rational matrix. It involves the knowledge of a complete set of solvents and the computation of the inverse of a block Vandermonde matrix. Numerical examples are given to illustrate the two results.

Malika Yaici | Kamel Hariche

[1] Benoit Boulet,et al. Robust controller order reduction , 2009, 2009 American Control Conference.

[2] J. F. Haffner,et al. Compensator design in the frequency domain using optimization , 2002, IEEE 2002 28th Annual Conference of the Industrial Electronics Society. IECON 02.

[3] João Carlos Basilio,et al. Inversion of polynomial matrices via state-space , 2002 .

[4] T. D. Lima,et al. A spectral approach to polynomial matrices solvents , 1996 .

[5] Kamel Hariche,et al. On solvents and Lagrange interpolating λ-matrices , 1988 .

[7] V. Kublanovskaya,et al. Methods and algorithms of solving spectral problems for polynomial and rational matrices , 1999 .

[8] M. J. Gibbard,et al. Numerical Operations with Polynomial Matrices , 1992 .

[9] Shou-Yuan Zhang. Inversion of polynomial matrices , 1987 .

[10] T. Ya. Kon'kova,et al. Inversion of polynomial and rational matrices , 1996 .

[11] Edgar Pereira,et al. On solvents of matrix polynomials , 2003 .

[12] Luca Bascetta,et al. On the design of the feedforward compensator in two-degree-of-freedom controllers , 2006 .

[13] P. Tzekis,et al. On the computation of the generalized inverse of a polynomial matrix , 2001 .

[14] P. Hippe,et al. Inversion of polynomial matrices by interpolation , 1992 .