On finite-time stability of homogeneous systems with multiplicative bounded function

摘要

In this paper, we study the finite-time stability of a class of nonlinear systems $dot{x}=f({x})=H(x)b(x)$, where $H$ is homogeneous and $b$ is bounded. We define the homogeneous extension of the non-homogeneous function $f$ and use this extension to prove that, under some conditions on b, if the system $dot{x} = f(x)$ is globally asymptotically stable, then it is finite-time stable. An example of global asymptotic stable system with some additional conditions is presented in the last section to illustrate the obtained results.