The recent developments in the research area of control systems and robotics are significantly advancing the field through innovative approaches and methodologies. A notable trend is the integration of advanced mathematical techniques, such as Koopman operator theory and Control Barrier Functions (CBFs), to address complex problems in system verification, safety, and stability. These methods are being refined to reduce conservatism and enhance the practical applicability of controlled-invariant safe sets, particularly in nonlinear and high-dimensional systems. Additionally, there is a growing emphasis on the development of learning-based control strategies that leverage machine learning techniques to handle model mismatch and actuator constraints, ensuring robustness and safety in robotic systems. The field is also witnessing advancements in the design and tuning of passivity-based controllers, which are crucial for optimal performance in robotics. Furthermore, the incorporation of active sensing strategies inspired by biological systems is providing new insights into the stabilization of certain classes of nonlinear systems. Overall, the research is moving towards more precise, less conservative, and biologically inspired control methodologies, with a strong focus on ensuring safety and stability in complex and dynamic environments.