On a construction of a non-linear control law for non-linear systems through Carleman Bilinearization

This paper deals with the problem of the construction of a non-linear control law for an analytic non-linear system through Carleman Bilinearization by using truncated Taylor series of the original non-linear system. The non-linear control law is constructed as a linear feedback control for the bilinearized approximated system that ensures local asymptotic stability inside the attraction domain. This attraction domain increases as the order truncated Taylor series become higher.