Nonlinear Output Feedback H_inf Control for Polynomial Nonlinear Systems

In this paper, we propose a computational scheme of solving the output feedback H∞ control problem for a class of nonlinear systems with polynomial vector field. The output feedback control design problem will be decomposed into a state feedback and an output estimation problems. Resorting to higher order Lyapunov functions, two Hamilton-JacobianIsaacs (HJI) inequalities are first formulated as semi-definite optimization conditions. Sum-of-squares (SOS) programming techniques are then applied to obtain computationally tractable solutions, from which a nonlinear control law will be constructed. The closed-loop system is asymptotically stabilizable by the nonlinear output feedback control and achieves good H∞ performance under the exogenous disturbances.