Robust stability of singularly perturbed systems with nonlinear uncertainties

The problem of robust stability of singularly perturbed systems with nonlinear uncertainties is considered. Via introducing a state transformation matrix and constructing the Lyapunov function, a stability bound epsiv* of the parameter epsiv is given such that the singularly perturbed systems are asymptotically stable. A sufficient condition is presented, which guarantee that the singularly perturbed systems are asymptotically stable. An example is illustrated to show how to apply the proposed results.