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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, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1976. With an appendix: “Limiting equations and stability of nonautonomous ordinary differential equations” by Z. Artstein; Regional Conference Series in Applied Mathematics. MR 0481301
  • [2] Gary H. Meisters, Jacobian problems in differential equations and algebraic geometry, Rocky Mountain J. Math. 12 (1982), no. 4, 679–705. MR 683862, https://doi.org/10.1216/RMJ-1982-12-4-679

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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