Robust control of a class of nonlinear uncertain systems

Robust control of a general class of uncertain nonlinear systems is investigated. The class of nonlinear systems includes many physical systems as special cases and has an important feature that the uncertainties in the system do not satisfy the matching conditions. Several robust control laws are proposed to make the system stable in the sense of either asymptotic stability or uniformly ultimately bounded stability. The results require no knowledge about the structure of the uncertainties. Although the uncertainties are assumed to be bounded in the Euclidean norm by a polynomial-type bounding function, there is no size restriction imposed on the bounding functions of the uncertainties. The extension to the trajectory tracking problem is also discussed