Hybrid systems are a type of dynamical system that combine continuous dynamics, described by differential equations, with discrete event dynamics, described by automata or logic rules. These systems are used to model complex systems that have both continuous and discrete behaviors, such as power systems, automotive systems, and biological systems. Hybrid systems research focuses on analyzing the behavior of these systems, developing methods for controlling them, and verifying their correctness. This research area often involves techniques from control theory, computer science, and mathematics to address the challenges of modeling and analyzing these systems. Overall, the goal of hybrid systems research is to develop tools and techniques that can be used to design and analyze complex systems that exhibit both continuous and discrete behaviors, leading to improved performance and reliability in a wide range of applications.