A Contraction Theory Approach to Singularly Perturbed Systems

In this technical note, we revisit standard results on singular perturbations and multiple time-scales using convergence analysis tools based on nonlinear contraction theory. Specifically, assuming that the fast and slow subsystems are each partially contracting, we obtain explicit bounds on the convergence rate of the trajectories to the slow manifold and on the asymptotic error between the trajectories of the singularly perturbed system and those of the reduced system. As an application example, we illustrate the design of a biomolecular insulation device.