ISS control laws for stabilizable retarded systems by means of the Liapunov-Razumikhin methodology

A disturbance adding to the control law is a typical situation in practice because of actuator errors. In this paper, state feedback control laws which provide input-to-state stability of the closed loop system with respect to a disturbance adding to the control law are investigated for state feedback stabilizable (in the case of disturbance equal to zero) retarded nonlinear systems. The formulas for the input-to-state stabilizing state feedback control law are provided by employing the Liapunov-Razumikhin methodology. An example taken from the past literature is investigated in details, showing the effectiveness and the applicability of the proposed control design.