Robust static output feedback design for polynomial nonlinear systems

A computational scheme of solving the nonlinear static output feedback design problems for a class of polynomial nonlinear systems is investigated in this paper. Sufficient conditions to achieve the closed-loop stability with or without H∞ performance are presented as state-dependent matrix inequalities, which provides an effective way for the application of the new sum of squares programming technique to obtain computationally tractable solutions. By introducing additional matrix variables, we succeed in eliminating the coupling between system matrices and the Lyapunov matrix. The proposed methodology is also extended to the synthesis for the parameter-dependent polynomial systems. Robust polynomial output feedback controller is designed in an efficient computational manner. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed methodology.