Robust control design for nonlinear uncertain systems in the absence of the generalized matching conditions

In this paper, we shall introduce and study a constructive procedure of designing robust control for uncertain nonlinear systems. The design procedure, called recursive-interlacing, is based on the Lyapunov´s direct method and includes recursive or backstepping designs as special cases. Nonlinear systems under investigation contain uncertainties that do not satisfy any of the previously developed conditions such as the matching conditions, the conditions of being equivalently matched, and the generalized matching conditions. Two classes of nonlinear uncertain systems of third order vector are presented for which robust controls are designed by the recursive-interlacing design. Due to the space limitation, only two of nonlinear third order vector systems are studied in details. Other classes of third order vector systems will be treated in upcoming papers