Analysis for a class of singularly perturbed hybrid systems via averaging
Wei Wang, Andrew R Teel, Dragan Nesic
AUTOMATICA | PERGAMON-ELSEVIER SCIENCE LTD | Published : 2012
A class of singularly perturbed hybrid dynamical systems is analyzed. The fast states are restricted to a compact set a priori. The continuous-time boundary layer dynamics produce solutions that are assumed to generate a well-defined average vector field for the slow dynamics. This average, the projection of the jump map in the direction of the slow states, and flow and jump sets from the original dynamics define the reduced, or average, hybrid dynamical system. Assumptions about the average system lead to conclusions about the original, higher-dimensional system. For example, forward pre-completeness for the average system leads to a result on closeness of solutions between the original and..View full abstract
Awarded by AFOSR
Awarded by NSF
Supported by the Australian Research Council under the Discovery Project and Future Fellow program, AFOSR (Grant FA9550-09-1-0203) and NSF (Grants ECCS-0925637 and CNS-0720842). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Faryar Jabbari under the direction of Editor Roberto Tempo.