Stability of a Class of Nonlinear Repetitive Processes with Application to Iterative Learning Control

Abstract

The paper considers a discrete repetitive process described by the state-space model with static nonlinearity satisfying quadratic constraints (in particular, the SISO case with the sector bounded nonlinearity). Based on the vector Lyapunov function approach developed by the authors, sufficient conditions of pass profile exponential stability are obtained in the form of linear matrix inequalities. These conditions are then applied to the design of an iterative learning control law for a simple nonlinear mechanical system.