Unified approach to H_∞-optimal control of singularly perturbed systems: Imperfect state measurements

The key contribution of the current paper is to present continuous-time and discrete-time singularly perturbed cases simultaneously under general imperfect state measurements using infinite-horizon formulations from the game theoretic approach, thereby highlighting the similarities and differences. We first show that as the small parameter ε approaches zero, the optimal disturbance attenuation levels for a full order system under a quadratic performance index converges to the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions. Then, we construct a controller based on the slow subsystem only, and obtain conditions under which it delivers a desired performance level even though the fast dynamics have been completely neglected. The ultimate performance level achieved by this `slow' controller can be uniformly improved upon, however, by a composite controller that uses some feedback from the output of the fast subsystem. We construct one such controller via a two step sequential procedure that uses static feedback from the fast system output and dynamic feedback from an appropriate slow system output, each one obtained by solving appropriate ε-independent lower dimensional H_∞-optimal control problems under some informational constraints.