Nonlinear H∞ almost disturbance decoupling

The L2-gain almost disturbance decoupling problem for SISO nonlinear systems is formulated. Sufficient conditions are identified for the existence of a parametrized state feedback controller such that the L2-gain from disturbances to output can be made arbitrarily small by increasing its gain. The controller is explicitly constructed using a Lyapunov-based recursive scheme. Sufficient conditions for the solvability of the H∞ almost disturbance decoupling problem and the explicit construction of the controller are given for a more restrictive class of nonlinear systems.