Stability robustness bounds of discrete two-time-scale systems

This note considers the problem of robustness of discrete two-time-scale systems. Robustness is first analyzed for a nominal system as the general ε-bound problem which characterizes an upper bound of the singular perturbation parameter. The stability robustness is then extended to handle the problem of systems subject to parameter variations. For any singular perturbation parameter bounded above by that obtained from the ε-bound problem, a stability robustness bound with respect to parameter variations is derived. The results include both unstructured and structured variations.