Reset Controller Analysis and Design for Unstable Linear Plants using Scaled Relative Graphs

Abstract

In this technical communique, we develop a graphical design procedure for reset controllers for unstable LTI plants based on recent developments on Scaled Relative Graph analysis, yielding an $L_2$-gain performance bound. The stabilizing controller consists of a second order reset element in parallel with a proportional gain. The proposed method goes beyond existing approaches that are limited to stable systems only, providing a well-applicable approach to design problems in practice where the plant is unstable.

5 pages, submitted on 16-06-2025 as a technical communique to Automatica. Second version with minor corrections 21-06-2025