Design of Output Feedback Controllers for Nonlinear Systems Using Sum-of-Squares-Programming

This paper presents an output feedback design approach for systems with non-polynomial nonlinearities using SOS-Programming. To this end a polynomial approximation of the system is determinded and the corresponding approximation error is computed. This error is used within the SOS-programm to determine a stabilizing output feedback and a Lyapunov funktion, which yield an as large as possible region of attraction of the equilibrium of the closed-loop original system. In order to influence the dynamics of the resulting closed-loop system, the linear part of the control law is assigned, which is used to assign desired eigenvalues to the linearization of the closed-loop system. If a dynamic output feedback is required for stabilization, the design method can be rewritten as a static output feedback desgin by adding the dynamic of the controller to the system description. A simple example illustrates the presented design approach.