Non-coercive Lyapunov functions forinfinite-dimensional systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Mironchenko, Andrii¹  Wirth, Fabian¹ 

[1] Univ Passau, Fac Comp Sci & Math, Innstr 33, D-94032 Passau, Germany

关键词: Nonlinear control systems;    Infinite-dimensional systems;    Lyapunov methods;    Global asymptotic stability;   

DOI  :  10.1016/j.jde.2018.11.026

来源: Elsevier

【 摘 要 】

We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied. For evolution equations in Banach spaces with Lipschitz continuous nonlinearities these additional assumptions become especially simple. The results encompass some recent results on linear switched systems on Banach spaces. Finally, we derive new non-coercive converse Lyapunov theorems and give some examples showing the necessity of our assumptions. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free