摘要：AbstractA new approach for modeling nonlinear impulsive system is suggested based on nonstandard analysis. Basic properties of the hyperreals in nonstandard analysis are revisited, and extended to define generalized functions via a sequence approach. The extended generalized functions yield a non unique definition for a Heaviside function and the delta function, which are used to characterize a nonsmooth vector field. By using these extended generalized function, a causal way for characterizing jumps in discontinuous systems follows. An example for a simple affine system illustrates the usefulness of this theoretical development.
