On the Gardner problem for phase-locked loops

DOI10.1134/S1064562419060218zbMath1447.93225OpenAlexW4236815453WikidataQ109649410 ScholiaQ109649410MaRDI QIDQ2191325

Yanyan Li

Publication date: 24 June 2020

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562419060218

zbMATH Keywords

global asymptotic stabilityphase-locked loopscylindrical phase spaceGardner problem

Mathematics Subject Classification ID

Frequency-response methods in control theory (93C80) Asymptotic stability in control theory (93D20)

Related Items (5)

Conditions for the existence of cycles in a system of differential equations ⋮ The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops ⋮ Hidden boundary of global stability in a counterexample to the Kapranov conjecture on the pull-in range ⋮ On the generalized Gardner problem for phase-locked loops in electrical grids ⋮ Theory of hidden oscillations and stability of control systems

Cites Work

• Multimode formation stability
• Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory
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