A note on the approximability property of nonlinear variable structure systems

Using a definition of approximability based on a suitable class of perturbations, the author proves that such a property is verified for nonlinear variable-structure systems of a general form. To do this he assumes the usual conditions of the theory of the equivalent control and uses the properties of the solution map of the initial-value problems. The results are compared with those of G. Bartolini and T. Zolezzi (J. Math. Anal. Appl., vol.118, no.1, p.42-62, 1986)