Hybrid systems refer to systems that combine continuous and discrete dynamics in a single model. These systems are used to model and analyze complex systems that exhibit both continuous behavior, such as physical processes, and discrete behavior, such as switching between different modes of operation. Research in hybrid systems focuses on developing mathematical models and analysis tools to study the interactions between the continuous and discrete components in these systems. This research area is interdisciplinary, drawing on principles from control theory, computer science, mathematics, and other fields. Applications of hybrid systems research include control systems for autonomous vehicles, robotics, power systems, and manufacturing systems, among others. The goal of this research is to improve the design, analysis, and performance of hybrid systems, ultimately leading to more efficient and reliable systems in various real-world applications.