论文标题
Lyapunov表征非线性无限维系统的均匀指数稳定性
Lyapunov characterization of uniform exponential stability for nonlinear infinite-dimensional systems
论文作者
论文摘要
在本文中，我们处理的是无限的非线性非线性正向完整的动力系统，这些动力系统受到外部干扰。我们首先将著名的Datko引理扩展到了考虑类别类别的框架。得益于这种概括，我们通过存在强制性和非可重的Lyapunov功能，提供了局部，半全球和全局指数稳定性的统一（关于干扰）的特征。通过某些应用程序关于1）具有分段延迟的非线性延迟系统的指数稳定性，2）针对半线性控制切换系统的指数稳定性保留，以及3）输入到状态到状态稳定性之间的链接。
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks to this generalization, we provide characterizations of the uniform (with respect to disturbances) local, semi-global, and global exponential stability, through the existence of coercive and non-coercive Lyapunov functionals. The importance of the obtained results is underlined through some applications concerning 1) exponential stability of nonlinear retarded systems with piecewise constant delays, 2) exponential stability preservation under sampling for semilinear control switching systems, and 3) the link between input-to-state stability and exponential stability of semilinear switching systems.
