| Title:
|
A spectral characterization of the behavior of discrete time AR–representations over a finite time interval (English) |
| Author:
|
Antoniou, E. N. |
| Author:
|
Vardulakis, A. I. G. |
| Author:
|
Karampetakis, N. P. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
5 |
| Year:
|
1998 |
| Pages:
|
[555]-564 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
discrete time auto regressive (AR) model |
| Keyword:
|
boundary conditions |
| Keyword:
|
finite and infinite spectral structure of the polynomial matrix |
| MSC:
|
62M10 |
| MSC:
|
65F30 |
| MSC:
|
93C55 |
| MSC:
|
93E10 |
| idZBL:
|
Zbl 1274.93174 |
| idMR:
|
MR1663736 |
| . |
| Date available:
|
2009-09-24T19:20:29Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135243 |
| . |
| Reference:
|
[1] Luenberger D. G.: Dynamic equations in descriptor form.IEEE Trans. Automat. Control 22 (1977), 3, 312–321 Zbl 0354.93007, MR 0479482, 10.1109/TAC.1977.1101502 |
| Reference:
|
[2] Luenberger D. G.: Boundary recursion for descriptor variable systems.IEEE Trans. Automat. Control 34 (1989), 3, 287–292 Zbl 0674.93043, MR 0980358, 10.1109/9.16418 |
| Reference:
|
[3] Lewis F. L.: Descriptor systems: Decomposition into forward and backward subsystems.IEEE Trans. Automat. Control 29 (1984), 2, 167–170 Zbl 0534.93013, MR 0736914, 10.1109/TAC.1984.1103467 |
| Reference:
|
[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 Zbl 0705.93058, MR 1048009, 10.1109/9.52316 |
| Reference:
|
[5] Lewis F. L.: A survey of linear singular systems.Circuits Systems Signal Process. 5 (1986), 1, 3–36 Zbl 0613.93029, MR 0893725 |
| Reference:
|
[6] Nikoukhah R., Willsky A., Levy B. C.: Boundary–value descriptor systems: well–posedness, reachability and observability.Internat. J. Control 46 (1987), 1715–1737 Zbl 0636.93055, MR 0917179, 10.1080/00207178708934005 |
| Reference:
|
[7] Gantmacher F. R.: Matrix Theory.Chelsea, New York 1971 |
| Reference:
|
[8] Gohberg I., Lancaster P., Rodman L.: Matrix Polynomials.Academic Press, New York 1982 Zbl 1170.15300, MR 0662418 |
| Reference:
|
[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 Zbl 0449.15015, MR 0611224, 10.1512/iumj.1981.30.30027 |
| Reference:
|
[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 Zbl 0496.15014, MR 0678825, 10.1080/03081088208817483 |
| Reference:
|
[11] Vardulakis A. I. G.: Linear Multivariable Control – Algebraic Analysis and Synthesis Methods.Wiley, New York 1991 Zbl 0751.93002, MR 1104222 |
| Reference:
|
[12] Willems J. C.: Paradigms and puzzles in the theory of dynamical systems.IEEE Trans. Automat. Control 36 (1991), 3, 259–294 Zbl 0737.93004, MR 1092818, 10.1109/9.73561 |
| . |
