Stabilizability of oscillatory systems: a classical approach supported by symbolic computation

In this paper we study the stabilization of planar single-input non-linear systems, whose linearization at the origin has purely immaginary eigenvalues. A classical recursive procedure based on polar coordinates transformation is applied to obtain some sufficient conditions. Then we focus on bilinear systems; a complete solution of the problem is given in this case. Explicit statements of the conditions are possible thanks to the use of symbolic computation packages.