Stabhyli -- a tool for automatic stability verification of non-linear hybrid systems. We present Stabhyli, a tool that automatically proves stability of non-linear hybrid systems. Hybrid systems are systems that exhibit discrete as well as continuous behavior. The stability property basically ensures that a system exposed to a faulty environment (e.g. suffering from disturbances) will be able to regain a “good” operation mode as long as errors occur not too frequently. Stabilizing Hybrid systems are omnipresent, for instance in control applications where a discrete controller is controlling a time-continuous process such as a car’s movement or a particular chemical reaction. We have implemented a tool to automatically derive a certificate of stability for non-linear hybrid systems. Certificates are obtained by Lyapunov theory combined with decomposition and composition techniques.