Constructive and discrete versions of the Lyapunov's stability theorem and the LaSalle's invariance theorem
Commun. Korean Math. Soc. 2002 Vol. 17, No. 1, 155-163
Printed March 1, 2002
Jaewook Lee
Pohang University of Science and Technology
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
MSC numbers : 37B55, 34D20, 37B25
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