Stabilization of nonlinear systems via the center manifold approach

This paper considers the problem of the stabilization of affine nonlinear control systems. First, we assume that the systems under investigation are of the generalized Byrnes–Isidori normal form. A new way to approximate the center manifold is proposed, which can reduce the error degree of the center manifold approximation. A new matrix product, called the semi-tensor product, is introduced to obtain the approximation of the center manifold. Then the Lyapunov function with homogeneous derivative (LFHD) is used to design a stable center manifold by state feedback control. Finally, the method is applied to general affine nonlinear control systems. c © 2008 Elsevier B.V. All rights reserved.