Stability of Zeno Equilibria in Lagrangian Hybrid Systems

This paper presents both necessary and sufficient conditions for the stability of Zeno equilibria in Lagrangian hybrid systems, i.e., hybrid systems modeling mechanical systems undergoing impacts. These conditions for stability are motivated by the sufficient conditions for Zeno behavior in Lagrangian hybrid systems obtained in [11]—we show that the same conditions that imply the existence of Zeno behavior near Zeno equilibria imply the stability of the Zeno equilibria. This paper, therefore, not only presents conditions for the stability of Zeno equilibria, but directly relates the stability of Zeno equilibria to the existence of Zeno behavior.