Vector Lyapunov functions for stability and stabilization of differential repetitive processes

Abstract

Differential repetitive processes arise in the analysis and design of iterative learning control algorithms. They belong to a class of mathematical models whose dynamic properties are defined by two independent variables, such as a time and a spatial coordinate, also known as 2D systems in the literature. Moreover, standard stability analysis methods cannot be applied to such processes. This paper develops a vector Lyapunov function-based approach to the exponential stability analysis of differential repetitive processes and applies the resulting conditions to develop linear matrix inequality based iterative learning control law design algorithms in the presence of model uncertainty.