Stabilisation for a class of non-linear systems with uncertain parameter based on centre manifold

The stabilisation problem of non-linear systems with multi-uncontrollable modes on the imaginary axes is studied. The relation between the centre manifold and the feedback law is given. By choosing the first coordinate function of the centre manifold, a state feedback law to stabilise the dynamics of the centre manifold is acquired. It can stabilise the full order system. This method is applied to stabilise non-linear systems with double Hopf bifurcation. The simulation shows the effectiveness of the method.