H∞-optimal control for singularly perturbed systems. II. Imperfect state measurements

The authors study H^∞-optimal control of singularly perturbed linear systems under general imperfect state measurements using infinite-horizon formulations. Using a differential game theoretic approach, they first show that, as the singular perturbation parameter ∈ approaches zero, the optimal disturbance attenuation level for the 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, they 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 by a composite controller that uses some feedback from the output of the fast subsystem. The authors construct one such controller, using a two-step sequential procedure, which uses static feedback from the fast output and dynamic feedback from an appropriate slow output, each obtained by solving appropriate ∈-independent lower-dimensional H^∞-optimal control problems