Extension of control Lyapunov functions to time-delay systems

The concept of control Lyapunov function has been proven a useful tool for designing robust control laws for nonlinear systems. This concept has been extended to time-delay systems in the form of control Lyapunov Razumikhin functions. We further develop this extension by introducing control Lyapunov Krasovsky functionals and show their use for robust stabilization of time-delay nonlinear systems. To further motivate the new concept we establish robustness properties for several control laws based on control Lyapunov Krasovsky functionals.