Robust stability of singularly perturbed systems with state delays

The stability of a linear two-time-scale system with state delays is studied. A delay-dependent sufficient condition for the stability bound ε* is given, such that the stability of the full-order model can be inferred from the analysis of its reduced-order model in separate time scales. The stability robustness problem of the same system is also discussed, where both the system matrices and time delays may be uncertain. Finally, an example is illustrated to show the applications of the results derived.