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.
|Original language||English (US)|
|Number of pages||5|
|Journal||Proceedings of the American Control Conference|
|State||Published - Dec 1 1999|