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

International audienceIn this paper, we study the finite-time stability of a class of nonlinear systems 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 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