Delay-range-dependent robust 2D iterative learning control for batch processes with state delay and uncertainties

• We model a batch process as 2 time dimensional state-space model with varying delays.
• We proposes a design for the integrated output feedback and iterative learning control (ILC) of batch processes.
• A sufficient criterion for delay-dependent H∞ noise attenuation is derived.
• Application to injection velocity control demonstrates the effectiveness and feasibility of the proposed design method.

This paper proposes the design of the integrated output feedback and iterative learning control (ILC) for batch processes with uncertain perturbations and interval time-varying delays, where the main idea is to transform the design into a robust delay-range-dependent H∞ control of a 2D system described by a state-space model with varying delays. A sufficient criterion for delay-dependent H∞ noise attenuation is derived through linear matrix inequality (LMI) by introducing a comprehensive 2D difference Lyapunov–Krasovskii functional candidate and adding a differential inequality to the difference in the Lyapunov function for the 2D system. Based on the criterion obtained, the delay-range-dependent output feedback controller combined with ILC is then developed. The developed system ensures that the closed-loop system for all admissible uncertainties is asymptotically stable and has a prescribed H∞ performance level in terms of the LMI constraint. The controller is obtained by solving an LMI optimization problem with simple calculations and less constraint conditions. Moreover, the conditions can also be directly extended from delay-range-dependent to general delay-dependent stability. Applications in injection velocity control demonstrate the effectiveness and feasibility of the proposed method.