SRG Analysis of Lur'e Systems and the Generalized Circle Criterion

Autor:	Krebbekx, Julius P. J., Tóth, Roland, Das, Amritam
Rok vydání:	2024
Předmět:	Electrical Engineering and Systems Science - Systems and Control Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. However, we show that the current SRG analysis suffers from some pitfalls that limit its applicability in analysing practical nonlinear systems. We overcome these pitfalls by modifying the SRG of a linear time invariant operator, combining the SRG with the Nyquist criterion, and apply our result to Lur'e systems. We thereby obtain a generalization of the celebrated circle criterion, which deals with broader class of nonlinearities, and provides (incremental) $L^2$-gain performance bounds. We illustrate the power of the new approach on the analysis of the controlled Duffing oscillator. Comment: 7 pages, 7 figures, submitted to European Control Conference 2025
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.18318 Zobrazit plný text záznamu View this record from Arxiv