Hybrid Dynamical Systems: Theory and Applications 

Course description

This graduate-level course aims to provide a set of mathematical tools to model, analyze, and design well-posed hybrid dynamical systems (systems that combine continuous-time dynamics and discrete-time dynamics) with suitable stability, robustness, and optimality properties. Topics that will be studied include: Basic properties of differential and difference equations and inclusions: Existence of solutions, uniqueness, Lyapunov stability theory, fixed point theorems, invariance principles. Introduction to basic hybrid systems that combine continuous-time and discrete-time dynamics: automata, switched systems, systems with timers and spatial regularization. Lyapunov theory for hybrid systems: Sufficient conditions for uniform asymptotic stability. Invariance principle for hybrid systems, and robustness corollaries.