A Generalized Nonuniform Contraction and Lyapunov Function | Zendy

Fangfang Liao | Zendy; Yongxin Jiang | Zendy; Zhiting Xie | Zendy

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A Generalized Nonuniform Contraction and Lyapunov Function

Author(s) -

Fangfang Liao,

Yongxin Jiang,

Zhiting Xie

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/613038

Subject(s) - mathematics , contraction (grammar) , lyapunov function , lyapunov exponent , function (biology) , mathematical analysis , nonlinear system , medicine , physics , quantum mechanics , evolutionary biology , biology

For nonautonomous linear equations x′=A(t)x, we give a completecharacterization of general nonuniform contractions in terms of Lyapunovfunctions. We consider the general case of nonuniform contractions, whichcorresponds 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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