A Generalized Nonuniform Contraction and Lyapunov Function

Fang-fang Liao, Yongxin Jiang and Zhiting Xie

Abstract and Applied Analysis, 2012, vol. 2012, 1-14

Abstract:

For nonautonomous linear equations , 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 -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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:613038

DOI: 10.1155/2012/613038

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