Dissipative Control for a Class of Uncertain Polynomial Nonlinear Systems

In this paper, the problem of dissipative control is investigated for continuous-time polynomial nonlinear systems with uncertainty. The purpose of the addressed problem is to design a state feedback controller such that the closed-loop system is asymptotically stable and the prescribed dissipativity performance is satisfied. By resorting to sum of squares method, sufficient conditions are derived for the existence of the anticipant controller taking advantage of the solution to the polynomial matrix inequality, thus the complex Hamilton-Jacobi inequalities and iterative programmings are avoided. Finally, two numerical examples are applied to confirm the effectiveness of the proposed method.