A tutorial on sum of squares techniques for systems analysis

This tutorial is about new system analysis techniques that were developed in the past few years based on the sum of squares decomposition. We present stability and robust stability analysis tools for different classes of systems: systems described by nonlinear ordinary differential equations or differential algebraic equations, hybrid systems with nonlinear subsystems and/or nonlinear switching surfaces, and time-delay systems described by nonlinear functional differential equations. We also discuss how different analysis questions such as model validation and safety verification can be answered for uncertain nonlinear and hybrid systems.