Robust disturbance suppression for nonlinear systems based on H_∞ control

The disturbance suppression problem for nonlinear systems is examined in this paper. We review the so-called nonstandard mixed sensitivity problem, which introduces an integrator to a selected weight, as well as the linear classical disturbance suppression problem and the linear H_∞ disturbance suppression problem. We extend this H_∞ problem to the nonlinear case, and present a method to reduce the order of the state feedback Hamilton-Jacobi PDE (Partial Differential Equation) for this nonlinear H_∞ problem by extending the concept of comprehensive stability [8] [7]. Finally, we investigate the structure of the output feedback H_∞ controller for disturbance suppression, and draw the conclusion that, as in the linear case, there must also be an integrator in the controller.