Introduction to the Stability of Time-Delay Systems.- Introduction to Analytic Curves.- Analytic Curve Perspective for Time-Delay Systems.- Computing Puiseux Series for a Critical Pair.- Invariance Property: A Unique Idea for Complete Stability Analysis.- Invariance Property for Critical Imaginary Roots (CIRs) with Index g = 1.- Invariance Property for Critical Imaginary Roots with Index n = 1.- Invariance Conjecture and Frequency-Sweeping Framework.- Complex Stability for Time-Delay Systems: A Unified Approach.- Extension to Neutral Time-Delay Systems.- Concluding Remarks and Further Perspectives.
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