Controlling oscillation by noncritical eigenvalue assignment

Linear feedback stabilization of nonlinear systems in critical cases (NSICC) is studied in this paper. The noncritical eigenvalues are assumed completely controllable. The stability and linear feedback stabilizability are attacked by means of center manifold method and Lyapunov stability analysis. The construction of linear feedback stabilizing law is given on the basis of noncritical eigenvalue assignment.