Homogeneous Domination and the Decentralized Control Problem for Nonlinear System Stabilization

This chapter gives an overview of constructive techniques for nonlinear dynamic system stabilization in the face of uncertainties and limited information from sensors. Such techniques have ultimately allowed for a loosening of the restrictions on the classes of nonlinear systems that could be systematically stabilized. The schemes discussed herein have the distinct commonality of dominating and thereby cancelling the undesirable effects of additive perturbations. Output feedback stabilization of highly nonlinear systems is discussed first, with the specific decentralized control problem setting then considered in addition to the output feedback issue. The schemes outlined in this chapter can be found in their entirety in several papers by the authors, with specific publications cited where applicable.