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Scaled Relative Graph of Normal Matrices
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The Scaled Relative Graph (SRG) is a geometric tool that maps the action of a multi-valued nonlinear operator onto the 2D plane, used to analyze the convergence of a wide range of iterative methods. As the SRG includes the spectrum for linear operators, we can view the SRG as a generalization of the spectrum to multi-valued nonlinear operators. In this work, we further study the SRG of linear operators and characterize the SRG of block-diagonal and normal matrices.
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Cited by 2 Pith papers
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The $\theta$-Symmetric SRG with Applications to Stability of Cactus Dynamic Networks
A theta-symmetric scaled relative graph is introduced, its phase is computed by semidefinite programming, and necessary and sufficient cyclic robust stability conditions are extended to cactus networks.
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A Dissipativity Framework for Constructing Scaled Graphs
A dissipativity-based LMI framework computes scaled graphs for LTI, reset, and piecewise-linear systems, with an exactness guarantee for normal LTI systems.
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