On the Synthesis of a Novel Nonlinear Feedback Control for Nonlinear Input-Affine Systems

In this paper, we have developed a new approach to determine a feedback control law of a nonlinear input affine system by the use of efficient mathematical tools: the Kronecker product, the non-redundant state formulation and the polynomial representation of the transformation to a reference linear model, as well as a polynomial form of the control law. This method consists, as first step, in determining a polynomial transformation of coordinates to an equivalent linear model. Then, the synthesis of an analytic feedback control law via this nonlinear transformation has been presented in the second method step. The advantage of the proposed approach is the convenience of its implementation, as it copes with the complex differential geometric formalism of the exact linearization feedback control. To illustrate the efficiency of the presented approach, we have been applied it to a second order nonlinear model whose simulations results are presented.