Robustness design for unknown uncertain singularly perturbed systems using random search methods via dithers and composite fuzzy control

In this paper, the system identification of the unknown uncertain singularly perturbed nonlinear system with external disturbance via new RO (random optimal) methods and a generalized model-based and composite fuzzy controller is designed to stabilize this system via H ^x theory. When the system cannot be stabilized by this composite fuzzy controller, a high frequency signal, commonly called dither, is simultaneously introduced to stabilize this system. If the frequency of dither is sufficiently high and the singular perturbation parameter is sufficiently small, the trajectory of the uncertain singularly perturbed dithered system and that of the uncertain singularly perturbed relaxed system can be made as close as desired. This enables us to get a rigorous prediction of the stability of the dithered system by establishing that of the relaxed system.