Journal Article

Lyapunov stability of abstract nonlinear dynamic system in Banach space

Gen‐Qi Xu and Siu Pang Yung

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 20, issue 1, pages 105-127
Published in print March 2003 | ISSN: 0265-0754
Published online March 2003 | e-ISSN: 1471-6887 | DOI: https://dx.doi.org/10.1093/imamci/20.1.105
Lyapunov stability of abstract nonlinear dynamic system in Banach space

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The Lyapunov stability theory for nonlinear time‐varying dynamic system in Banach space is given in this paper. The Lyapunov stable theorem and the Barbashin–Krasovskii–LaSalle invariant set principle in classical theory are extended to infinite‐dimensional Banach space. Under the assumptions of the existence of solution and the additive property of motions, sufficient and necessary conditions for uniform stability and uniform asymptotic stability are obtained, and the Lyapunov functions are explicitly constructed. This extension can be used as a criterion of stability for continuous and discontinuous systems.

Keywords: Banach space; abstract nonlinear dynamic equation; Lyapunov stability

Journal Article.  0 words. 

Subjects: Mathematics

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