  This paper presents a new systematic framework for nonlinear singularly
perturbed systems in which state-dependent perturbation functions are used
instead of constant perturbation coefficients. Under this framework, general
results are obtained for the global robust stability and input-to-state
stability of nonlinear singularly perturbed systems. Interestingly, the
proposed methodology provides innovative solutions beyond traditional singular
perturbation theory for emerging control problems arising from nonlinear
integral control, feedback optimization, and formation-based source seeking.
