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CONSTRUCTIVE AND DISCRETE VERSIONS OF THE LYAPUNOV′S STABILITY THEOREM AND THE LASALLE′S INVARIANCE THEOREM
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 Title & Authors
CONSTRUCTIVE AND DISCRETE VERSIONS OF THE LYAPUNOV′S STABILITY THEOREM AND THE LASALLE′S INVARIANCE THEOREM
Lee, Jae-Wook;
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 Abstract
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.
 Keywords
non-autonomous discrete dynamical system;Lyapunov function;exponentially stable fixed point;
 Language
English
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 References
1.
Geometrical Methods in the Theory of Ordinary Differential Equations, 1977.

2.
DIFFERENTIAL GEOMETRY CONTROL THEORY, 1983.

3.
Applied methematical sciences, 1986. vol.42.

4.
Nonliear Systems, 1992.

5.
Stability by Lyapunov's Direct Method, 1961.

6.
IEEE Trans. on Circuits and System, 2001. vol.48. 1, pp.51-66 crossref(new window)

7.
J. Dynamical System, Measurement, Control, 1981. vol.112. pp.119-125

8.
Proc. IEEE, 1985. vol.73. pp.1703-1715 crossref(new window)