Geodesic
A spectral characterization of the behavior of discrete time AR–representations over a finite time interval
Kybernetika, Tome 34 (1998) no. 5, pp. 555-564
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.
In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.
Classification : 62M10, 65F30, 93C55, 93E10
Keywords: discrete time auto regressive (AR) model; boundary conditions; finite and infinite spectral structure of the polynomial matrix 
@article{KYB_1998_34_5_a4,
     author = {Antoniou, E. N. and Vardulakis, A. I. G. and Karampetakis, N. P.},
     title = {A spectral characterization of the behavior of discrete time {AR{\textendash}representations} over a finite time interval},
     journal = {Kybernetika},
     pages = {555--564},
     year = {1998},
     volume = {34},
     number = {5},
     mrnumber = {1663736},
     zbl = {1274.93174},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1998_34_5_a4/}
}
TY  - JOUR
AU  - Antoniou, E. N.
AU  - Vardulakis, A. I. G.
AU  - Karampetakis, N. P.
TI  - A spectral characterization of the behavior of discrete time AR–representations over a finite time interval
JO  - Kybernetika
PY  - 1998
SP  - 555
EP  - 564
VL  - 34
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/KYB_1998_34_5_a4/
LA  - en
ID  - KYB_1998_34_5_a4
ER  - 
%0 Journal Article
%A Antoniou, E. N.
%A Vardulakis, A. I. G.
%A Karampetakis, N. P.
%T A spectral characterization of the behavior of discrete time AR–representations over a finite time interval
%J Kybernetika
%D 1998
%P 555-564
%V 34
%N 5
%U http://geodesic.mathdoc.fr/item/KYB_1998_34_5_a4/
%G en
%F KYB_1998_34_5_a4
Antoniou, E. N.; Vardulakis, A. I. G.; Karampetakis, N. P. A spectral characterization of the behavior of discrete time AR–representations over a finite time interval. Kybernetika, Tome 34 (1998) no. 5, pp. 555-564. http://geodesic.mathdoc.fr/item/KYB_1998_34_5_a4/

[1] Luenberger D. G.: Dynamic equations in descriptor form. IEEE Trans. Automat. Control 22 (1977), 3, 312–321 | DOI | MR | Zbl

[2] Luenberger D. G.: Boundary recursion for descriptor variable systems. IEEE Trans. Automat. Control 34 (1989), 3, 287–292 | DOI | MR | Zbl

[3] Lewis F. L.: Descriptor systems: Decomposition into forward and backward subsystems. IEEE Trans. Automat. Control 29 (1984), 2, 167–170 | DOI | MR | Zbl

[4] Lewis F. L., Mertzios B. G.: On the analysis of discrete linear time–invariant singular systems. IEEE Trans. Automat. Control 35 (1990), 4, 506–511 | DOI | MR | Zbl

[5] Lewis F. L.: A survey of linear singular systems. Circuits Systems Signal Process. 5 (1986), 1, 3–36 | MR | Zbl

[6] Nikoukhah R., Willsky A., Levy B. C.: Boundary–value descriptor systems: well–posedness, reachability and observability. Internat. J. Control 46 (1987), 1715–1737 | DOI | MR | Zbl

[7] Gantmacher F. R.: Matrix Theory. Chelsea, New York 1971

[8] Gohberg I., Lancaster P., Rodman L.: Matrix Polynomials. Academic Press, New York 1982 | MR | Zbl

[9] Gohberg I., Kaashoek M. A., Lerer L., Rodman L.: Common multiples and common divisors of matrix polynomials. I. Spectral method. Indiana J. Math. 30 (1981), 321–356 | DOI | MR | Zbl

[10] Gohberg I., Kaashoek M. A., Lerer L., Rodman L.: Common multiples and common divisors of matrix polynomials. II. Van der Monde and resultant matrices. Linear and Multilinear Algebra 12 (1982), 159–203 | DOI | MR | Zbl

[11] Vardulakis A. I. G.: Linear Multivariable Control – Algebraic Analysis and Synthesis Methods. Wiley, New York 1991 | MR | Zbl

[12] Willems J. C.: Paradigms and puzzles in the theory of dynamical systems. IEEE Trans. Automat. Control 36 (1991), 3, 259–294 | DOI | MR | Zbl