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Question of global asymptotic stability in state-varying nonlinear systems


Authors: Mau-Hsiang Shih and Jinn Wen Wu
Journal: Proc. Amer. Math. Soc. 122 (1994), 801-804
MSC: Primary 39A11; Secondary 39B12, 58F10
DOI: https://doi.org/10.1090/S0002-9939-1994-1204384-3
MathSciNet review: 1204384
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Abstract | References | Similar Articles | Additional Information

Abstract: A problem raised by LaSalle (i.e., a discrete counterpart of the Jacobian problem in differential equations) concerning the global asymptotic stability in state-varying nonlinear systems is settled. A global asymptotic stability criterion for state-varying systems based on vector energy functions is introduced.


References [Enhancements On Off] (What's this?)

  • [1] J. P. LaSalle, The stability of dynamical systems, CBMS-NSF Regional Conf. Ser. in Appl. Math., vol. 25, SIAM, Philadelphia, PA, 1976. MR 0481301 (58:1426)
  • [2] G. H. Meisters, Jacobian problems in differential equations and algebraic geometry, Rocky Mountain J. Math. 12 (1982), 679-705. MR 683862 (84c:58048)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1204384-3
Keywords: Global asymptotic stability, LaSalle's problem, state-varying system, spectral radius
Article copyright: © Copyright 1994 American Mathematical Society

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