| Title:
|
Some remarks on matrix pencil completion problems (English) |
| Author:
|
Loiseau, Jean-Jacques |
| Author:
|
Zagalak, Petr |
| Author:
|
Mondié, Sabine |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
40 |
| Issue:
|
6 |
| Year:
|
2004 |
| Pages:
|
[665]-680 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The matrix pencil completion problem introduced in [J. J. Loiseau, S. Mondié, I. Zaballa, and P. Zagalak: Assigning the Kronecker invariants to a matrix pencil by row or column completions. Linear Algebra Appl. 278 (1998)] is reconsidered and the latest results achieved in that field are discussed. (English) |
| Keyword:
|
matrix pencils |
| Keyword:
|
the Kronecker invariants |
| Keyword:
|
matrix completion |
| Keyword:
|
linear systems |
| Keyword:
|
state feedback |
| MSC:
|
15A22 |
| MSC:
|
93B25 |
| MSC:
|
93B52 |
| MSC:
|
93C05 |
| MSC:
|
93D20 |
| idZBL:
|
Zbl 1249.93081 |
| idMR:
|
MR2120389 |
| . |
| Date available:
|
2009-09-24T20:04:58Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135625 |
| . |
| Reference:
|
[1] Baragaña I., Zaballa I.: Column completion of a pair of matrices.Linear and Multilinear Algebra 27 (1990), 243–273 Zbl 0704.15010, MR 1065067, 10.1080/03081089008818016 |
| Reference:
|
[2] Cabral I., Silva F. C.: Unified theorems on completions of matrix pencils.Linear Algebra and its Applications 159 (1991), 43–54 Zbl 0738.15007, MR 1133334 |
| Reference:
|
[3] Gantmacher F. R.: Matrix Theory.Vol. II. Chelsea, New York 1974 |
| Reference:
|
[4] Hautus M. L. J., Heymann M.: Linear feedback: an algebraic approach.SIAM J. Control Optim. 7 (1978) 50–63 Zbl 0385.93015, MR 0476024 |
| Reference:
|
[5] Herrera A., Mondié S.: On the complete controllability indices assignment problem.To appear |
| Reference:
|
[6] Heymann M.: Controllability indices and feedback simulation.SIAM J. Control Optim. 14 (1981), 4, 769–789 MR 0439296, 10.1137/0314050 |
| Reference:
|
[7] Kailath T.: Linear Systems.Englewood Cliffs, Prentice–Hall, NJ 1980 Zbl 0870.93013, MR 0569473 |
| Reference:
|
[8] Kronecker L.: Algebraische reduction der schaaren bilinearer formen.S.-B. Akad. Berlin 1890, pp. 763–776 |
| Reference:
|
[9] Kučera V.: Assigning the invariant factors by feedback.Kybernetika 17 (1981), 2, 118–127 MR 0624204 |
| Reference:
|
[10] Loiseau J. J.: Contribution à l’étude des sous–espaces presque invariants.Thèse de Doctorat de l’Université de Nantes, 1986 |
| Reference:
|
[11] Loiseau J. J.: Pole placement and related problems.Kybernetika 28 (1992), 2, 90–100 Zbl 0762.93037, MR 1169212 |
| Reference:
|
[12] Loiseau J. J., Mondié S., Zaballa, I., Zagalak P.: Assigning the Kronecker invariants to a matrix pencil by row or column completions.Linear Algebra Appl. 278 (1998), 327–336 MR 1637316 |
| Reference:
|
[13] Loiseau J. J., Zagalak P.: On a special case of model matching.Internat. J. Control 77 (1994), 2, 164–172 MR 2035020, 10.1080/00207170310001647678 |
| Reference:
|
[14] Mondié S.: Contribución al estudio de modificaciones estructurales de sitemas lineales.Ph.D. Thesis, Dept. Ing. Electrica, CINVESTAV del IPN, México, D.F. 1996 |
| Reference:
|
[15] Mondié S., Loiseau J. J.: Structure assignment of state–output systems by choice of the output equation.In: Proc. IFAC Conference on System Structure and Control, Nantes 1995, pp. 172–177 |
| Reference:
|
[16] Mondié S., Loiseau J. J.: Simultaneous zeros and controllability indices assignment through nonregular static state feedback.In: Proc. 36th IEEE Conference on Decision and Control, San Diego 1997 |
| Reference:
|
[17] Mondié S., Loiseau J. J.: Structure assignment of right invertible implicit systems through nonregular static state feedback.In: Proc. European Control Conference, Brussels 1997 |
| Reference:
|
[18] Mondié S., Zagalak, P., Kučera V.: State feedback in linear control theory.Linear Algebra and its Applications 317 (2000), 177–192 Zbl 0967.93022, MR 1782208 |
| Reference:
|
[19] Morse A. S.: Structural invariants of linear multivariable systems.SIAM J. Control 11 (1973), 446–465 Zbl 0259.93011, MR 0386762, 10.1137/0311037 |
| Reference:
|
[20] Rosenbrock H. H.: State Space and Multivariable Theory.Nelson, London 1970 Zbl 0246.93010, MR 0325201 |
| Reference:
|
[21] Sá E. Marques de: Imbedding conditions for $\lambda $-matrices.Linear Algebra Appl. 24 (1979) , 33–50 Zbl 0395.15009, MR 0524824, 10.1016/0024-3795(79)90145-9 |
| Reference:
|
[22] Thompson R. C.: Interlacing inequalities for invariant factors.Linear Algebra Appl. 24 (1979), 1–31 Zbl 0395.15003, MR 0524823, 10.1016/0024-3795(79)90144-7 |
| Reference:
|
[23] Wolovich W. A.: Multivariable Linear Systems.Springer Verlag, 1974 MR 0359881 |
| Reference:
|
[24] Zaballa I.: Interlacing inequalities and control theory.Linear Algebra Appl. 87 (1987), 113–146 MR 0941293 |
| Reference:
|
[25] Zaballa I.: Feedback invariants of matrix quadruple completions.Linear Algebra Appl. 292 (1999), 73–97 Zbl 0952.93053, MR 1689305 |
| Reference:
|
[26] Zagalak P., Loiseau J. J.: Invariant Factors Assignment in Linear Systems.In: Proc. International Symposium on Implicit and Nonlinear Systems, The University of Texas, Arlington 1992, pp. 197–204 |
| . |
