A robust stabilization using state feedback with feedforward

In a general nonlinear control system a stabilizing control strategy is often possible if complete information on external inputs affecting the system is available. Assuming that measurements of persistent disturbances are available it is shown that the existence of a smooth uniform control Lyapunov function implies the existence of a stabilizing state feedback with feedforward control which is robust with respect to measurement errors and external disturbances. Conversely, using differential inclusions parameterized as nonlinear systems with state and disturbance measurement errors, it is shown that there exists a smooth uniform control Lyapunov function if there is a robustly stabilizing state feedback with feedforward. This paper demonstrates that if there exists a smooth control Lyapunov function for a general nonlinear system with persistent disturbances for which one has previously designed a feedback controller, a feedforward always exists to be augmented for stability.