Project H4 develops concepts, theories and algorithms used for the automated verification and analysis as well as tool-supported design of a broad range of hybrid systems exhibiting convergence and stability properties. Effectiveness and efficiency of system analysis beyond the state of the art is achieved through the identification and exploitation of powerful state-space reducing abstractions, novel transformations, and guided composition and decomposition techniques. Project H4's method portfolio allows the analysis and design of robust and cost-efficient hybrid systems.