Razumikhin and Krasovskii approaches for safe stabilization

This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin Krasovskii approaches, we propose novel control Lyapunov functions/functionals for problem barrier problem. The proposed extend existing ones from delay-free case to case, allow designing stabilizing controllers in closed-form. Since analytical solutions optimal are hard be achieved, a sliding mode based approach is developed merge functions/functionals. Based on surface functional, feedback law established investigate objectives simultaneously. In particular, properties functional analyzed, further how construct discussed. Finally, approaches illustrated via two numerical examples connected cruise automotive systems synchronization multi-agent