Explore the mathematical framework and tools for analyzing and synthesizing robust hybrid feedback control systems in this 40-minute conference talk. Delve into the world of hybrid dynamical systems, which combine continuous and impulsive dynamics to describe complex systems. Learn about asymptotic stability and invariance of sets, and see how these tools are applied to real-world scenarios ranging from genetic networks to power systems. Discover the scope of hybrid systems research, recent contributions to the field, and common features in applications. Examine autonomous hybrid systems, differential equations with multistable elements, and modeling techniques for switched and impulsive systems. Gain insights into the general control problem, Lyapunov stability theorem, and hybrid basic conditions. Investigate sequential compactness theorem, invariance principle, and their consequences. Conclude with a practical application to boost converters and a comprehensive introduction to hybrid systems and modeling. Read more