Parametrization of nonlinear stabilizing control laws for bifurcations and critical systems

A parametrization of a large class of nonlinear feedback control laws which stabilize unstable critical systems and the corresponding bifurcations is proposed. The feedback control consists of quadratic and cubic forms in the state variables. The parametrization makes use of the modal decomposition-based multilinear form representations, for which an algorithm is developed. The parametrization is then obtained by using the algorithm to implement the specifications of the design parameters within the quadratic and cubic forms.<>