Asymptotic Stability of Limit Cycles in Hybrid Systems with Explicit Logic States

This work pertains to the study of stability of limit cycles for hybrid systems with explicit logic states within a hybrid systems framework. We first focus on constructing the hybrid systems with explicit logic states and revealing basic properties of limit cycles. Application to model switched systems under dwell-time switching as such a hybrid system is provided. In addition, we establish sufficient and necessary conditions for stability of the limit cycles relying on Poincaré maps. Examples illustrate the results. A discussion about the case of systems with nonunique solutions is also included.