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Soft and Hard Scaled Relative Graphs for Nonlinear Feedback Stability
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This article presents input-output stability analysis of nonlinear feedback systems based on the notion of soft and hard scaled relative graphs (SRGs). The soft and hard SRGs acknowledge the distinction between incremental positivity and incremental passivity and reconcile them from a graphical perspective. The essence of our proposed analysis is that the separation of soft SRGs or hard SRGs of two open-loop systems on the complex plane guarantees closed-loop stability. The main results generalize an existing soft SRG separation theorem for bounded open-loop systems which was proved based on interconnection properties of soft SRGs under a chordal assumption. By comparison, our analysis does not require this chordal assumption and applies to possibly unbounded open-loop systems based on their hard SRGs.
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Cited by 3 Pith papers
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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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