Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 418091, 11 pages
http://dx.doi.org/10.1155/2012/418091
Research Article

-Stability of Multistable Nonlinear Discrete-Time Systems

Zhishuai Ding,1 Guifang Cheng,1,2 and Xiaowu Mu1

1Department of Mathematics, Zhengzhou University, Zhengzhou, Hennan 450001, China
2Physical Engineering College, Zhengzhou University, Zhengzhou, Hennan 450001, China

Received 8 June 2011; Accepted 28 October 2011

Academic Editor: Baodong Zheng

Copyright © 2012 Zhishuai Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of -stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.