On stabilization of non linear systems by using carleman linearization and periodic systems theory

This paper deals with the Standard Truncated Carleman Bilinearization and its use to stabilize a non-linear system. The Carleman Bilinearization states that every analytic n-dimensional nonlinear system is equivalent to an infinite dimensional bilinear system. As a result, the new system is made up of a state linear, a control linear and a bilinear matrices in the state space format. In this work we truncate this bilinearization and by using a periodic control law we transform this bilinear system into a periodic linear system, thus we can use periodic linear systems theory in order to find the conditions in periodic control law for stabilize the new periodic system and after that apply this law in the original non linear system.