Gap metric robustness of a backstepping control design

A robust backstepping controller is designed for a plant in strict-feedback form which is perturbed by both input and measurement disturbances. The closed-loop is shown to be gain-function stable, and stable under Lipschitz conditions on the nonlinearities. This controller is also shown to achieve stability for any perturbed plant whose gap distance from the strict-feedback system is less than some computable quantity.