Nonlinear feedback control of stabilization problem via formal linearization using Taylor expansion

In this paper we consider a nonlinear feedback control problem for stabilizing multidimensional nonlinear systems using a formal linearization method based on Taylor expansion. Our goal is to design a nonlinear feedback control which stabilizes the nonlinear system in wider region of state space with less restricted conditions. The single-input multidimensional nonlinear system is transformed into an approximated bilinear system with respect to a formal linearization function by a formal linearization method using Taylor expansion. Substituting the ordinary LQ control function to the bilinear terms, a linear system with respect to the formal linearization function is derived and a feedback control is obtained. Finally, we illustrate some simulations to verify our approach.