Robust control of nonlinear uncertain systems without generalizedmatching conditions

A novel procedure, called recursive-interlacing procedure, is proposed for designing globally stabilizing robust control. The procedure introduces new interlacing steps and combines them with the existing recursive or backstepping design. It is shown by examining all possible third-order vector systems that the procedure is applicable to systems not satisfying any of the existing structural conditions, that is, to systems in which uncertainties are potentially anywhere and of any bounding function. By its nature, the procedure is not limited to systems of any specific order; it either produces stabilizing control or reveals certain measure of unstabilizability, and it includes recursive design as a special case