Design of a robust H<inf>∞</inf> repetitive control system with time-delay

This paper investigates the problem of designing a robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> repetitive control system with periodic time-delay. Firstly, a continuous-discrete two-dimensional (2D) model with time-delay is constructed to describe the control and learning actions of the system. Then, by choosing an appropriate Lyapunov functional, LMI-based sufficient stability conditions for asymptotic stability and satisfactory H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> tracking performance of the 2D model is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.