An Algorithmic Approach to Stability Verification of Hybrid Systems: A Summary

This paper summarizes results related to a novel algorithmic approach for verifying stability of hybrid systems. The traditional approach based on Lyapunov function search suffers from several disadvantages --- it relies on the user expertise to obtain good templates for the Lyapunov function; further, an unsuccessful attempt at instantiating the templates provides no insights into the choice of better templates. To overcome these difficulties, the algorithmic approach relies on an abstraction refinement framework which systematically searches for a proof and provides insights to the user in the event of a failure to prove stability. We summarize the new foundations, techniques and software tools that we have developed for the algorithmic approach to stability verification.