| Title:
|
Stability zones for discrete time Hamiltonian systems (English) |
| Author:
|
Răsvan, Vladimir |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
5 |
| Year:
|
2000 |
| Pages:
|
563-573 |
| . |
| Category:
|
math |
| . |
| MSC:
|
39A10 |
| idZBL:
|
Zbl 1090.39503 |
| idMR:
|
MR1822826 |
| . |
| Date available:
|
2008-06-06T22:27:39Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107771 |
| . |
| Reference:
|
References 1. M.G. Krein: Foundations of theory of $\lambda$-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). |
| Reference:
|
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). MR 0364739 |
| Reference:
|
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). MR 0157072 |
| Reference:
|
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). MR 0867871 |
| Reference:
|
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). MR 1097966 |
| Reference:
|
5. W. Kratz: Quadratic Functionals in Variational Analysis and Control Theory.Akademie Verlag, Berlin, 1995. Zbl 0842.49001, MR 1334092 |
| Reference:
|
6. C.D. Ahlbrandt, A.C. Peterson: Discrete Hamiltonian systems: Difference Equations, Continued Fractions and Riccati Equations.Kluwer, Boston, 1996. Zbl 0860.39001, MR 1423802 |
| Reference:
|
7. M. Bohner: Linear Hamiltonian Difference Systems: disconjugacy and Jacobi-type conditions.J. Math.Anal.Appl 199, pp. 804-826, 1996. MR 1386607 |
| Reference:
|
8. M. Bohner, O. Došlý: Disconjugacy and transformations for symplectic systems.Rocky Mountain J. Math. 27, pp. 707-743, 1997. MR 1490271 |
| Reference:
|
9. O. Došlý: Transformations of linear Hamiltonian difference systems and some of their applications.J. Math.Anal.Appl. 191, pp. 250-265, 1995. MR 1324013 |
| Reference:
|
10. A. Halanay, V. Ionescu: Time - varying Discrete Hamiltonian Systems.Computers Math. Appl. 36, 10-12, pp. 307-326, 1998. Zbl 0933.39032, MR 1666149 |
| Reference:
|
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. MR 1764958 |
| Reference:
|
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. |
| Reference:
|
13. L. Erbe S. Hilger: Sturmian theory on measure chains.Diff. Equations Dynam. Syst. 1,3, pp. 223-244, 1993. MR 1258900 |
| Reference:
|
14. S. Hilger: Analysis on measure chains - a unified approach to continuous and discrete calculus.Results Math. 18, pp. 18-56, 1990. MR 1066641 |
| Reference:
|
15. A. Halanay, Vl. Răsvan: Stability and Boundary Value Problems for Discrete-time Linear Hamiltonian Systems.Dynamic. Syst. Appl. 8, pp. 439-459, 1993. MR 1722972 |
| Reference:
|
16. A. Halanay, D. Wexler: Qualitative theory of pulse systems.(in Romanian) Editura Academiei, Bucharest, 1968 (Russian version by Nauka, Moscow, 1971). MR 0233016 |
| Reference:
|
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). |
| Reference:
|
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). MR 0264447 |
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