Stability zones for discrete time Hamiltonian systems
Archivum Mathematicum (2000)
- Volume: 036, Issue: 5, page 563-573
- ISSN: 0044-8753
Access Full Article
topHow to cite
topRăsvan, Vladimir B.. "Stability zones for discrete time Hamiltonian systems." Archivum Mathematicum 036.5 (2000): 563-573. <http://eudml.org/doc/248557>.
@article{Răsvan2000,
author = {Răsvan, Vladimir B.},
journal = {Archivum Mathematicum},
keywords = {discrete Hamiltonian; strong stability},
language = {eng},
number = {5},
pages = {563-573},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stability zones for discrete time Hamiltonian systems},
url = {http://eudml.org/doc/248557},
volume = {036},
year = {2000},
}
TY - JOUR
AU - Răsvan, Vladimir B.
TI - Stability zones for discrete time Hamiltonian systems
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 5
SP - 563
EP - 573
LA - eng
KW - discrete Hamiltonian; strong stability
UR - http://eudml.org/doc/248557
ER -
References
top- References 1. M.G. Krein, Foundations of theory of -zones of stability of a canonical system of linear differential equations with periodic coeffcients, (in Russian). In ”In Memoriam A.A. Andronov”, pp. 413-98, USSR Acad.Publ. House, Moscow, 1955 (English version in AMS Translations 120(2): 1-70, 1983). (1955)
- 2. V.A. Yakubovich, V.M. Staržinskii, Linear differential equations with periodic coeffcients, (in Russian). Nauka Publ. House, Moscow, 1972 (English version by J.Wiley, 1975). (1972) MR0364739
- 3. M.G. Krein, V.A. Yakubovich, Hamiltonian Systems of Linear Differential Equations with Periodic Coeffcients, (in Russian). In ”Proceedings Int’l Conf. on Nonlin. Oscillations”, vol.1, Ukrainian SSR Acad. Publ. House, Kiev, pp. 277-305, 1963 (English version AMS Translations 120(2): 139-168, 1983). (1963) MR0157072
- 4. V.A. Yakubovich, Linear quadratic optimization problem and frequency domain theorem for periodic systems I, Siberian Math. Journ., 27, 4, pp. 186-200, 1986 (in Russian). (1986) MR0867871
- V.A. Yakubovich, Linear quadratic optimization problem and frequency domain theorem for periodic systems II, Siberian Math. Journ., 31, 6, pp. 176-191, 1990 (in Russian). (191,) MR1097966
- 5. W. Kratz, Quadratic Functionals in Variational Analysis and Control Theory, Akademie Verlag, Berlin, 1995. (1995) Zbl0842.49001MR1334092
- 6. C.D. Ahlbrandt, A.C. Peterson, Discrete Hamiltonian systems: Difference Equations, Continued Fractions and Riccati Equations, Kluwer, Boston, 1996. (1996) Zbl0860.39001MR1423802
- 7. M. Bohner, Linear Hamiltonian Difference Systems: disconjugacy and Jacobi-type conditions, J. Math.Anal.Appl 199, pp. 804-826, 1996. (199,) MR1386607
- 8. M. Bohner, O. Došlý, Disconjugacy and transformations for symplectic systems, Rocky Mountain J. Math. 27, pp. 707-743, 1997. (1997) MR1490271
- 9. O. Došlý, Transformations of linear Hamiltonian difference systems and some of their applications, J. Math.Anal.Appl. 191, pp. 250-265, 1995. (191,) MR1324013
- 10. A. Halanay, V. Ionescu, Time - varying Discrete Hamiltonian Systems, Computers Math. Appl. 36, 10-12, pp. 307-326, 1998. (1998) Zbl0933.39032MR1666149
- 11. A. Halanay, Vl. Răsvan, Oscillations in Systems with Periodic Coeffcients and Sector-restricted Nonlinearities, in Operator Theory: Advances and Applications vol. 117, pp. 141-154, Birkhauser Verlag, Basel, 2000. MR1764958
- 12. B. Aulbach S. Hilger, A Unified Approach to Continuous and Discrete Dynamics, Colloquia Mathematica Societatis Janos Bolyai, 53. Qualitative theory of differential equations, Szeged, Hungary, 1988. (1988)
- 13. L. Erbe S. Hilger, Sturmian theory on measure chains, Diff. Equations Dynam. Syst. 1,3, pp. 223-244, 1993. (1993) MR1258900
- 14. S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. 18, pp. 18-56, 1990. (1990) MR1066641
- 15. A. Halanay, Vl. Răsvan, Stability and Boundary Value Problems for Discrete-time Linear Hamiltonian Systems, Dynamic. Syst. Appl. 8, pp. 439-459, 1993. (1993) MR1722972
- 16. A. Halanay, D. Wexler, Qualitative theory of pulse systems, (in Romanian) Editura Academiei, Bucharest, 1968 (Russian version by Nauka, Moscow, 1971). (1968) MR0233016
- 17. F.R. Gantmakher, M.G.Krein, Oscillation matrices and kernels and small oscillations of mechanical systems, (in Russian) 2nd ed. GITTL, Moscow, 1950 (German version by Akademie Verlag, Berlin, 1960). (1950)
- 18. I. Ts. Gohberg, M.G. Krein, Theory and applications of Volterra operators in Hilbert space, (in Russian) Nauka, Moscow, 1967 (English version in AMS Translations Math. Monographs vol. 24, Providence R.I. 1970). (1967) MR0264447
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.