Construction of a smooth Lyapunov function for an asymptotically stable set

Tadek Nadzieja

Czechoslovak Mathematical Journal (1990)

  • Volume: 40, Issue: 2, page 195-199
  • ISSN: 0011-4642

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Nadzieja, Tadek. "Construction of a smooth Lyapunov function for an asymptotically stable set." Czechoslovak Mathematical Journal 40.2 (1990): 195-199. <http://eudml.org/doc/13843>.

@article{Nadzieja1990,
author = {Nadzieja, Tadek},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonsingular; invariant set; asymptotically stable set; Lyapunov function; Riemannian manifold; complete vector field},
language = {eng},
number = {2},
pages = {195-199},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Construction of a smooth Lyapunov function for an asymptotically stable set},
url = {http://eudml.org/doc/13843},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Nadzieja, Tadek
TI - Construction of a smooth Lyapunov function for an asymptotically stable set
JO - Czechoslovak Mathematical Journal
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 2
SP - 195
EP - 199
LA - eng
KW - nonsingular; invariant set; asymptotically stable set; Lyapunov function; Riemannian manifold; complete vector field
UR - http://eudml.org/doc/13843
ER -

References

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  1. N. P. Bhatia G. P. Szegö, Stability Theory of Dynamical Systems, Springer-Verlag, Berlin-Heidelberg-New York 1970. (1970) Zbl0213.10904MR0289890
  2. J. Kurzweil, On the inversion of Lyapunov's second theorem on stability of motion, Czechoslovak Math. J. 81 (1956), 217-259, 455-473 (in Russian; Summary in English, ibidem, 474-484). English transl.: Amer. Math. Soc. Transl., Ser. II, 24 (1963), 19-77. (1956) 
  3. J. L. Massera, 10.2307/1969955, Ann. of Math. 64 (1956), 182-206; Erratum, Ann. of Math. 68 (1958), 202. (1956) Zbl0070.31003MR0079179DOI10.2307/1969955
  4. J. L. Massera, Converse theorems of Lyapunov's second method, Symp. Intern. Ecuac. Dif. Ordin., Mexixo 1961 (1962), 158-163. (1961) Zbl0102.30603MR0132259
  5. K. P. Persidskii, On a theorem of Lyapunov, Dokl. Akad. Nauk SSSR 14 (1937), 541-544 (in Russian). (1937) 
  6. F. W. Wilson, 10.1090/S0002-9947-1969-0251747-9, Trans. Am. Math. Soc. 139 (1969), 413-428. (1969) Zbl0175.20203MR0251747DOI10.1090/S0002-9947-1969-0251747-9
  7. V. I. Zubov, Methods of A. M. Lyapunov and their Application, Leningrad 1957 (in Russian). English transl.: Groningen 1964. (1957) MR0086966

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