Soft-hard equivalence in circular scaled graph containment bypasses computational constraints for feedback stability, while hyperbolically convex conics yield tighter bounds for nonsymmetric cases.
The scaled relative graph of a linear operator
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Scaled relative graphs are extended to normed spaces via directional pairings from regular pairings, yielding geometric containment tests for contraction and monotonicity.
Mirror symmetry of SRG uncertainty regions about the theta-axis gives necessary and sufficient conditions for robust nonsingularity and stability of LTI systems via the Davis-Wielandt shell.
Exact and computable constructions of Scaled Relative Graphs for closed linear operators are given via maximum and minimum gain computations, with a Bounded Real Lemma route for state-space models.
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Scaled Graph Containment for Feedback Stability: Soft-Hard Equivalence and Conic Regions
Soft-hard equivalence in circular scaled graph containment bypasses computational constraints for feedback stability, while hyperbolically convex conics yield tighter bounds for nonsymmetric cases.
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Scaled Relative Graphs in Normed Spaces
Scaled relative graphs are extended to normed spaces via directional pairings from regular pairings, yielding geometric containment tests for contraction and monotonicity.
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Symmetry Is Almost All You Need: Robust Stability with Uncertainty Induced by Symmetric SRG Regions
Mirror symmetry of SRG uncertainty regions about the theta-axis gives necessary and sufficient conditions for robust nonsingularity and stability of LTI systems via the Davis-Wielandt shell.
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Computable Characterisations of Scaled Relative Graphs of Closed Operators
Exact and computable constructions of Scaled Relative Graphs for closed linear operators are given via maximum and minimum gain computations, with a Bounded Real Lemma route for state-space models.