Almost disturbance decoupling for a class of high-order nonlinear systems

The problem of almost disturbance decoupling with internal stability (ADD) is formulated, in terms of an L-2-L-2p (instead of an L-2) gain, for a clas s of high-order nonlinear systems which consist of a chain of power integra tors perturbed by a lower-triangular vector field. A significant feature of the systems considered in the paper is that they are neither feedback line arizable nor affine in the control input, which have been two basic assumpt ions made in all the existing ADD nonlinear control schemes. Using the so-c alled adding a power integrator technique developed recently in [15], we so lve the ADD problem via static smooth state feedback, under a set of growth conditions that can be viewed as a high-order version of the feedback line arization conditions. We also show how to explicitly construct a smooth sta te feedback controller that attenuates the disturbance's effect on the outp ut to an arbitrary degree of accuracy, with internal stability.