Tracking control of nonlinear systems with disturbance attenuation

Sufficient geometric conditions are given which lead to the explicit construction of a state feedback tracking control for single-input single-output nonlinear systems with bounded unmodeled disturbances entering nonlinearly. For any initial condition the output asymptotically tracks a bounded reference signal with bounded time derivatives with an arbitrary attenuation of the influence of the disturbance. The sufficient conditions are weaker than those presented in R. Marino et al. (1989) and the technique of proof is also different. Singular perturbation techniques are not used; special coordinates in which the control algorithm and a Lyapunov function are recursively built are determined