CONSTRUCTIVE AND DISCRETE VERSIONS OF THE LYAPUNOV′S STABILITY THEOREM AND THE LASALLE′S INVARIANCE THEOREM

Title & Authors
CONSTRUCTIVE AND DISCRETE VERSIONS OF THE LYAPUNOV′S STABILITY THEOREM AND THE LASALLE′S INVARIANCE THEOREM
Lee, Jae-Wook;

Abstract
The purpose of this paper is to establish discrete versions of the well-known Lyapunovs stability theorem and LaSalles 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
Cited by
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3.
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4.
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5.
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