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Hybrid dynamical systems can exhibit many unique phenomena, such as Zenobehavior. Zeno behavior is the occurrence of infinite discrete transitions infinite time. Zeno behavior has been likened to a form of finite-time asymptoticstability, and corresponding Lyapunov theorems have been developed. In thispaper, we propose a method to construct Lyapunov functions to prove Zenostability of compact sets in cyclic hybrid systems with parametricuncertainties in the vector fields, domains and guard sets, and reset mapsutilizing sum-of-squares programming. This technique can easily be applied tocyclic hybrid systems without parametric uncertainties as well. Examplesillustrating the use of the proposed technique are also provided.

A Sum-of-Squares Approach to the Analysis of Zeno Stability in Polynomial Hybrid Systems