An LMI approach to H∞ control for affine nonlinear system

This paper studies the problem of H_∞ control for a affine nonlinear system with disturbance. Based on HJI inequation, a sufficient condition is presented in the form of LMI to ensure the nonlinear H_∞ controller´s existence. The nonlinear H_∞ controller can efficiently attenuate the effect of disturbance on system output. Simultaneously, it can guarantee the closed loop system is globally asymptotically stable at the origin. Using matlab software, it is not easy to solve the LMI problem, therefore the presented method is feasible. Finally, a numerical example simulation is provided to illustrate the effectiveness of the method.