Robust L2 Gain Design for A Class of Nonlinear Systems with Uncertain Input Dynamics

Abstract

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 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.