Control Design Based on Sum of Squares Programming for Non-affine in Input Systems

This paper addresses the state feedback control synthesis for the class of nonaffine in input systems using the sum of squares (SOS) programming. Due to the nature of these systems, the SOS control design technique becomes a non-convex problem. In order to circumvent this issue, two input-affine approximations are proposed, both based on linearization. In order to ensure better approximations, we propose the inclusion of new restrictions, which are inserted into the SOS program. Two examples are given to provide analytical and graphical illustration of the given approaches. It is performed the stability analysis of the open-loop system by estimating its region of attraction (RoA) and their enlargement, achieved with a state feedback controller.