Abstract:
Comparison of algorithms for computing infinite structural indices of polynomial matrices Keywords Linear systems, polynomial matrices, structural indices, decoupling control, numerical linear algebra, computer-aided control system design. A new algorithm is proposed to compute the infinite structural indices of a polynomial matrix, i.e. the algebraic and geometric multiplicities of its poles and zeros at infinity. Infinite structural indices of polynomial matrices play a key role when solving e.g. multivariable decoupling control problems. The algorithm is based on numerically stable operations only, and takes full advantage of the block Toeplitz structure of a constant matrix built directly from the polynomial matrix coefficients. Comparative numerical examples and a full computational complexity analysis indicate that the Toeplitz algorithm can be viewed as a competitive alternative to the well-known state-space pencil matrix algorithm for obtaining structural indices. 1
Citations
|
37
|
Discrete Linear Control. The Polynomial Equation Approach
– Kucera
- 1979
|
|
37
|
The computation of Kronecker's canonical form of a singular
– Dooren
- 1979
|
|
27
|
Linear Multivariable Control: Algebraic Analysis and Synthesis Methods
– Vardulakis
- 1991
|
|
23
|
Matrix Theory
– Gantmacher
- 1959
|
|
21
|
The eigenstructure of an arbitrary polynomial matrix
– Dooren, Dewilde
- 1983
|
|
5
|
An Algorithm for Polynomial Matrix Factor Extraction
– Henrion, Sebek
- 2000
|
|
5
|
On the Determination of the Smith-MacMillan Form of a Rational Matrix from its Laurent Expansion
– Dooren, Dewilde, et al.
- 1979
|
|
3
|
The Polynomial Toolbox for Matlab. Version 2.5
– Polyx
- 2001
|
|
2
|
Factorizations and linear system solvers for matrices with Toeplitz structure. Slicot Working Note, No. 2000-2, Katholieke Universiteit
– Kressner, Dooren
- 2001
|
|
1
|
Desoer C.A., Multivariable Feedback Systems
– Callier
- 1982
|
|
1
|
Extraction of Infinite Zeros of Polynomial Matrices
– J
- 2000
|
|
1
|
Christov N.D. and Konstantinov M.M.,. Computational Methods for Linear Control Systems
– Hr
- 1991
|
|
1
|
Algorithm for decoupling and pole assignment of linear multivariable systems. Research Report
– Zúñiga, Ruiz-León, et al.
- 2002
|
