Global stabilization with almost disturbance decoupling of a class of uncertain non-linear systems

In this paper we study the global stabilization of a class of non-linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy. The class of non-linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order. Although the plants considered are non-linear, the compensator developed here is linear. Our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback. Model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so-called ‘matching conditions’ and/or by treating a family of plants  for which a single controller simultaneously globally exponentially stabilizes all the plants in  while achieving almost disturbance decoupling of the output.