Stability analysis of nonlinear multiparameter singularly perturbed systems

Asymptotic stability of nonlinear multiparameter singularly perturbed systems is analyzed. Sufficient conditions for existence of a Lyapunov function and uniform asymptotic stability are derived. The new feature of these conditions over earlier results is that there is no restriction on the relative magnitudes of the small singular perturbation parameters. Moreover, the class of systems under consideration can be nonlinear in both the slow and fast variables, while earlier results were limited to systems linear in the fast variables.