Synchronization of Singularly Perturbed Systems with Time Scales

Synchronization problems of continuous and discrete singularly perturbed systems are studied in this paper with singular perturbations and time scales (SPaTS) technique. The dynamics of leader and followers are decomposed into pure-slow and pure-fast subsystems. Locally optimal decentralized tracking sub-controllers are synthesized respectively to asymptotically synchronize each subsystem of follower. A composite control protocol is proposed to synchronize the original dynamics of each follower with the leader's dynamics. Both analogous and digital flight control systems for aircraft formation flying are utilized to verify the effectiveness of the control schemes.