# $H_\infty$ Performance Analysis for Almost Periodic Piecewise Linear Systems with Application to Roll-to-Roll Manufacturing Control

## TL;DR

This paper develops an $H_
abla$ performance analysis method for almost periodic piecewise linear systems with uncertain switching, enabling improved disturbance rejection in manufacturing control applications like roll-to-roll processing.

## Contribution

It introduces a novel $H_
abla$ analysis approach and synthesizes practical controllers for APPLSs, addressing the gap in disturbance rejection guarantees.

## Key findings

- Proposed $H_
abla$ method reduces conservativeness in controller design.
- Experimental results demonstrate superior performance over baseline controllers.
- Application to roll-to-roll manufacturing shows practical effectiveness.

## Abstract

An almost periodic piecewise linear system (APPLS) is a type of piecewise linear system where the system cyclically switches between different modes, each with an uncertain but bounded dwell-time. Process regulation, especially disturbance rejection, is critical to the performance of these advanced systems. However, a method to guarantee disturbance rejection has not been developed. The objective of this study is to develop an $H_\infty$ performance analysis method for APPLSs, building on which an algorithm to synthesize practical $H_\infty$ controllers is proposed. As an application, the developed methods are demonstrated with an advanced manufacturing system -- roll-to-roll (R2R) dry transfer of two-dimensional materials and printed flexible electronics. Experimental results show that the proposed method enables a less conservative and much better performing $H_\infty$ controller compared with a baseline $H_\infty$ controller that does not account for the uncertain system switching structure.

---
Source: https://tomesphere.com/paper/2508.21199