Control Lyapunov Functionals and robust stabilization of nonlinear time-delay systems

In this work, we provide necessary and sufficient Lyapunov-like conditions for the existence of a stabilizing feedback law for uncertain control systems described by retarded functional differential equations. A methodology for the construction of control Lyapunov functionals for uncertain triangular nonlinear time-delay systems is provided. Moreover, the method leads to the explicit design of robust nonlinear controllers for the class of time-delay nonlinear systems with a triangular structure.