Global Feedback Stabilization of Non-zero Equilibrium Points of Polynomial System Using Dissipativity Theory

Abstract

Nonlinear polynomial systems can present complex behavior and high sensitivity with the variation of its initial condition. These issues can make it difficult to design a controller with the objective of stabilizing the system around an equilibrium point. This work aims to apply an iterative strategy known in literature to the problem closed-loop stabilization of a nonlinear polynomial system around the origin and to other equilibrium points using the notion of Equilibrium-Independent Dissipativity (EID) and Sum of Squares (SOS) decomposition concepts. The controller design is performed computationally, using the SOSTOOLS Toolbox. The results obtained for the open-loop and closed-loop system are compared in order to validate the performance of the controller designed by the proposed method. The analysis shows the effectiveness of the iterative method for polynomial systems, resulting in a great simplification in the controller design for a nonlinear system.