Singular nonlinear H-infinity optimal control problem

The theory of nonlinear H∞ of optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for solvability of the state feedback singular H∞ control problem. The resulting state feedback is then used to construct a dynamic compensator solving the nonlinear output feedback H∞ control problem by applying the certainty equivalence principle.