Lipschitz stability of nonlinear systems of differential equations. (English) Zbl 0595.34054
The authors define a new notion of stability - uniform Lipschitz stability (ULS) for nonlinear systems of differential equations (1) , where and exists and is continuous on , , , , and is the solution of (1) with . Definition. The zero solution of (1) is said to be (ULS) if there exists and such that whenever and . Several criteria for the (ULS) are obtained. It is shown by examples that the (ULS) coincides with the uniform stability in the linear case, which means that the (ULS) is a nonlinear phenomenon. The relationship between (ULS) and various types of stability notions is illustrated by a diagram.
|34D10||Stability perturbations of ODE|