Scaled Relative Graphs and Dynamic Integral Quadratic Constraints: Connections and Computations for Nonlinear Systems
This work addresses the challenge of graphical analysis for nonlinear systems in control theory, offering incremental improvements by connecting SRGs with existing IQC methods.
The paper tackled the problem of analyzing and designing nonlinear systems by introducing a systematic method to compute scaled relative graphs (SRGs) using dynamic integral quadratic constraints (IQCs), resulting in tractable overbounds and a new graphical interpretation for feedback stability in Lur'e-type systems.
Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints (IQCs). These constraints are exploited via application of the S-procedure to compute tractable SRG overbounds. In particular, we show that the multipliers associated with the IQCs define regions in the complex plane. Soft SRG computations are formulated through frequency-domain conditions, while hard SRGs are obtained via hard factorizations of multipliers and linear matrix inequalities. The overbounds are used to derive an SRG-based feedback stability result for Lur'e-type systems, providing a new graphical interpretation of classical IQC stability results with dynamic multipliers.