Robust stability of singularly perturbed impulsive systems under nonlinear perturbation

The robust stability problem for singularly perturbed impulsive systems under nonlinear perturbation is considered. The uncertainties are assumed to be limited by their upper norm bound. By applying the vector Lyapunov function method and a two-time scale comparison principle, a sufficient condition that ensures robust exponential stability for sufficiently small singular perturbation parameter is derived. Moreover, the stability bound of the singular perturbation parameter can be obtained by solving a set of matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.