Implementation of the Exact Feedback Linearization Method in Non-Affine Systems under Uncertainty

For multichannel nonlinear systems of one class functioning under conditions of parametric and external disturbances, the synthesis problem for tracking systems within the framework of the dynamic feedback linearization method is considered. The class of considered systems with identical elements of the relative degree vector reduced to a complete (i.e., without the internal dynamics subsystem) equivalent block-canonical input-output form in the coordinate basis of mixed variables (functions of state variables, external actions, and their derivatives) is formalized. The basic (typical) conditions are listed under which dynamic feedback is implemented, ensuring a linear form of the closed tracking system and, consequently, exponential stabilization of tracking errors invariantly with respect to external uncontrolled disturbances. The design peculiarity of the tracking system implies using mixed variable observers with piecewise linear corrective actions that allow, without any dynamic disturbance generators and identifiers of uncertain parameters introduced, restoring the mixed variables and uncertain inputs, by the estimates of which the feedback is closed. The principal result is related to weakening the basic conditions and expanding admissible systems from the class under consideration that are linearized by dynamic output feedback under conditions of incomplete measurements and parametric uncertainty of input control channels.