Globally Uniform Stability of a Class of Continuous Cascaded Systems
一类连续级联系统的全局一致稳定性

Globally uniform stability is obtained for a class of nonlinear continuous cascaded systems by using homo- geneous properties of homogeneous systems.It is assumed that the driving subsystem and the driven subsystem have globally uniformly asymptotical stability and have certain degrees of homogeneity.If the cascaded term also satisfies a homogeneous inequality,then the cascaded system has globally uniformly asymptotical stability.Furthermore,if both the driving subsystem and the driven subsystem have the negative degrees of homogeneity,the cascaded system is globally uniformly finite-time stable.Compared with the conventional ISS assumption or the growth assumption of the cascaded term,the homogeneous inequality assumption of the cascaded term is easier to verify.Furthermore,the proposed method can be applied not only to the Lipschitz continuous systems but also to the non-Lipschitz continuous systems.Two examples are given to verify the effectiveness of the method.