Nonlinear robust control: An SOS — Based approach

This paper presents a method for the analysis and control design of polynomial nonlinear systems in the presence of uncertainty and external disturbance. Based on the sum of squares (SOS) technique, sufficient conditions for robust stabilization without and with H∞ performance via state feedback are formulated in terms of state dependent linear matrix inequalities (LMIs). Such convex conditions can be solved by semidefinite programming relaxations based on the SOS programming, by which the obstacle in solving Hamilton-Jacobi Equations/Inequalities (HJEs/HJIs) disappear. A numerical example is presented to illustrate the effectiveness of the approach.