Robust L2 gain design for a class of nonlinear systems with uncertain input dynamics

In this paper, robust L₂ gain design problem is investigated for a class of nonlinear systems with uncertain input dynamics. For the input uncertainty, the control direction is not required to be known but the zero dynamics is restricted to be input-to-state stable (ISS). A robust dynamical controller is designed by constructing a positive definite function guaranteeing the Barbalat´s condition such that the closed-loop system satisfies robust L₂ gain constraint, and a parameter adaptive function is introduced to the control law for compensation of the unknown control direction. Furthermore, the control law is extended to the high dimension systems.