Output feedback stabilization of singularly perturbed systems

Output feedback control of linear time-invariant singularly perturbed systems is studied. The set of all compensators that stabilize a singularly perturbed system while preserving its two-time-scale structure is parametrized. The parametrization is used to show that any two-frequency-scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure. In this procedure, a fast (high-frequency) compensator is designed first to stabilize the fast model of the system. Then, a strictly proper slow (low-frequency) compensator is designed to stabilize a modified slow model. The parallel connection of the two compensators forms a two-frequency-scale stabilizing compensator for the singularly perturbed system.