On the design of stabilizing controllers for singularly perturbed systems

The robustness of output feedback control designs for singularly perturbed systems based on the reduced systems is discussed. A frequency-domain approach is presented to determine the conditions for the stability of linear time-invariant systems subject to neglected high-frequency dynamics. In contrast with the qualitative analyses for robust stability that have appeared in the literature, this approach gives an explicit, computable bound on unmodeled dynamics which does not destabilize the systems. Stability conditions for various feedback control schemes are presented. It is noted that the approach, extended to systems with mixed singular-regular perturbations, can be used to derive the robust stability condition