Input-to-State Stabilizing a General Nonlinear System with Time-Varying Input Delay and Disturbances

Abstract

We investigate input-to-state stabilization for a general nonlinear system with input delay and disturbances. With an infinite-dimensional backstepping transformation, the original system is transferred to a target system. A delay-compensating and disturbances attenuating control law is designed for this kind of nonlinear systems. Stability of the target system is first proved by constructing a Lyapunov functional. Equivalence of norms for original and target system is deduced. Further, input-to-state stabilization for the original system under the delay-compensating control law is drawn.