Stability zones for discrete time Hamiltonian systems

Vladimir B. Răsvan

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 5, page 563-573
  • ISSN: 0044-8753

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Răsvan, 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

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  1. References 1. M.G. Krein, Foundations of theory of λ -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. 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. 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. 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
  5. 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
  6. 5. W. Kratz, Quadratic Functionals in Variational Analysis and Control Theory, Akademie Verlag, Berlin, 1995. (1995) Zbl0842.49001MR1334092
  7. 6. C.D. Ahlbrandt, A.C. Peterson, Discrete Hamiltonian systems: Difference Equations, Continued Fractions and Riccati Equations, Kluwer, Boston, 1996. (1996) Zbl0860.39001MR1423802
  8. 7. M. Bohner, Linear Hamiltonian Difference Systems: disconjugacy and Jacobi-type conditions, J. Math.Anal.Appl 199, pp. 804-826, 1996. (199,) MR1386607
  9. 8. M. Bohner, O. Došlý, Disconjugacy and transformations for symplectic systems, Rocky Mountain J. Math. 27, pp. 707-743, 1997. (1997) MR1490271
  10. 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
  11. 10. A. Halanay, V. Ionescu, Time - varying Discrete Hamiltonian Systems, Computers Math. Appl. 36, 10-12, pp. 307-326, 1998. (1998) Zbl0933.39032MR1666149
  12. 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
  13. 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) 
  14. 13. L. Erbe S. Hilger, Sturmian theory on measure chains, Diff. Equations Dynam. Syst. 1,3, pp. 223-244, 1993. (1993) MR1258900
  15. 14. S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. 18, pp. 18-56, 1990. (1990) MR1066641
  16. 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
  17. 16. A. Halanay, D. Wexler, Qualitative theory of pulse systems, (in Romanian) Editura Academiei, Bucharest, 1968 (Russian version by Nauka, Moscow, 1971). (1968) MR0233016
  18. 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) 
  19. 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

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