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
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd