대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제17권1호
  • /
  • Pages.155-163
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  • 2002
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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CONSTRUCTIVE AND DISCRETE VERSIONS OF THE LYAPUNOV′S STABILITY THEOREM AND THE LASALLE′S INVARIANCE THEOREM

  • Lee, Jae-Wook (Department of Industrial Engineering, Pohang University of Science and Technology)
  • 발행 : 2002.01.01
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초록

The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.

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참고문헌

  1. Geometrical Methods in the Theory of Ordinary Differential Equations V. I. Arnold
  2. DIFFERENTIAL GEOMETRY CONTROL THEORY Asymptotic stability and feedback stabilization R. W. Brockett(eds.);R. S. Millman(eds.);H. J. Sussmann(eds.)
  3. Applied methematical sciences v.42 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields J. Guckenheimer;P. Homes
  4. Nonliear Systems H. K. Khalil
  5. Stability by Lyapunov's Direct Method J. P. La Salle;S. Lefschetz
  6. IEEE Trans. on Circuits and System v.48 no.1 Convergent regions of Newton homotopy methods: theory and computational applications Jaewook Lee;H. -D. Chiang https://doi.org/10.1109/81.903187
  7. J. Dynamical System, Measurement, Control v.112 Sastry A new feedback method for dynamic control of manipulators M. Takegaki;S. Sastry
  8. Proc. IEEE v.73 Direct methods for transient stability analysis of power systems: Recent results P. P. Varaiya;F. F. Wu;R. L. Chen https://doi.org/10.1109/PROC.1985.13366

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  3. Criterion for limit cycle-free state-space digital filters with external disturbances and generalized overflow non-linearities 2016, https://doi.org/10.1177/0142331216680287
  4. Criterion for the limit cycle free state-space digital filters with external disturbances and quantization/overflow nonlinearities vol.33, pp.1, 2016, https://doi.org/10.1108/EC-01-2015-0011
  5. A Note on the Induced $${\varvec{l}}_\infty $$ l ∞ Stability of Fixed-Point Digital Filters Without Overflow Oscillations and Instability Due to Finite Wordlength Effects vol.36, pp.3, 2017, https://doi.org/10.1007/s00034-016-0348-x
  6. Criterion for realizing state-delayed digital filters subjected to external interference employing saturation arithmetic pp.1573-7543, 2018, https://doi.org/10.1007/s10586-018-2530-3
  7. Induced l∞ stability of fixed-point digital filters without overflow oscillations and instability due to finite word length effects vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1847-2012-51