Exponential stability of nonlinear differential equations in the presence of perturbations or delays

The exponential stability of nonlinear nonautonomous nonsmooth differential equations in finite dimensional linear spaces is investigated. It turns out that exponential stability is preserved under sufficiently small perturbations or delays. Explicit estimates for the relation between the exponential decay rates and the size of the perturbation or delay are presented. The results are valid for differential equations given by Lipschitz continuous vector fields.