Rocky Mountain Journal of Mathematics

Qualitative Analysis of Nonlinear Systems by the Method of Matrix Lyapunov Functions

A.A. Martynyuk

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 25, Number 1 (1995), 397-415.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181072291

Digital Object Identifier
doi:10.1216/rmjm/1181072291

Mathematical Reviews number (MathSciNet)
MR1340016

Zentralblatt MATH identifier
0841.34057

Subjects
Primary: 34D20: Stability

Keywords
Nonlinear systems matrix Lyapunov function stability

Citation

Martynyuk, A.A. Qualitative Analysis of Nonlinear Systems by the Method of Matrix Lyapunov Functions. Rocky Mountain J. Math. 25 (1995), no. 1, 397--415. doi:10.1216/rmjm/1181072291. https://projecteuclid.org/euclid.rmjm/1181072291


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References

  • M.Z. Djordjevic, Stability analysis of large-scale systems whose subsystems may be unstable, Large-Scale Systems 5 (1983), 252-262.
  • Lj.T. Grujić, On large-scale systems stability, Proceedings 12th World Congress, IMACS 1 (1988), 224-229.
  • --------, Stabilnost Velikih Sistema, Beograd, Masinski Facultet, 1974.
  • L.T. Grujić, A.A. Martynyuk and M. Ribbens-Pavella, Large-scale systems stability under structural and singular perturbations, Springer Verlag, Berlin, 1987.
  • A.M. Lyapunov, General problem of stability of motion, Harkov Math. Soc., published in Collected Papers 2, Ac. of Sci. USSR, Moscow-Leningrad (1956), 5-163 (in Russian).
  • A.A. Martynyuk, Stability of motion of complex systems, Nauk. Dumbka, Kiev, 1975.
  • --------, Lyapunov matrix function, Nonlinear Anal. 8 (1984), 1223-1226.
  • --------, On Lyapunov matrix function and stability of motion, DAN USSR 280 (1985), 1062-1066.
  • --------, On application of the Lyapunov matrix function in the theory of stability, Nonlinear Anal. 9 (1985), 1495-1501.
  • A.A. Martynyuk and R. Gutovsky, Integral inequalities and stability of motion, Nauk. Dumka, Kiev, 1979.
  • A.A. Martynyuk and V.G. Miladzhanov, On the theory of stability large-scale systems under structural perturbations, Automatica J. IFAC 6 (1991), 32-38.
  • --------, Sufficiently conditions absolutely of stability large-scale systems under structural perturbations, Automatica J. IFAC 15 (1991), 12-18.
  • V.M. Matrosov, L.Yu. Anapolskii and S.N. Vasilyev, Method of comparison in mathematical theory of systems, Nauka, Novosibirsk, 1980.
  • A.N. Michel and R.K. Miller, Qualitative analysis of large-scale dynamical systems, Academic Press, New York, 1977.
  • H. Poincare, Sur les courbes definies par une equation differentielle, Journal de Mathematiques 7 (1881-1882), no. Serie 3, 375-422, 8, 251-296.
  • D.D. Siljak, Large-scale dynamic systems: stability and structure, North Holland, New York, 1978.