Open Access
2012 A Generalized Nonuniform Contraction and Lyapunov Function
Fang-fang Liao, Yongxin Jiang, Zhiting Xie
Abstr. Appl. Anal. 2012(SI07): 1-14 (2012). DOI: 10.1155/2012/613038


For nonautonomous linear equations x = A ( t ) x , we give a complete characterization of general nonuniform contractions in terms of Lyapunov functions. We consider the general case of nonuniform contractions, which corresponds to the existence of what we call nonuniform ( D , μ ) -contractions. As an application, we establish the robustness of the nonuniform contraction under sufficiently small linear perturbations. Moreover, we show that the stability of a nonuniform contraction persists under sufficiently small nonlinear perturbations.


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Fang-fang Liao. Yongxin Jiang. Zhiting Xie. "A Generalized Nonuniform Contraction and Lyapunov Function." Abstr. Appl. Anal. 2012 (SI07) 1 - 14, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1261.34043
MathSciNet: MR3004916
Digital Object Identifier: 10.1155/2012/613038

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI07 • 2012
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