On stabilization and output tracking of a class of nonlinear systems via new backstepping-like methods

In this article, controller design for a class of nonlinear systems is considered. The strict feedback form is a special case of this class and the proposed method is an extension to the backstepping method. In general form, the proposed method suggests a dynamical controller which has one state less than the system. However, the controller order is not fixed and it may be less than the general form. In a special case, the proposed controller reduces into a static function which is the original backstepping method. The proposed method can be used for stabilization and output tracking for this class which may be quite complicated or even impossible with regular methods. The proposed control strategy is based on the stability of the augmented states. In case that the assumption does not hold, another strategy is suggested to be used for stabilization.