@inproceedings{9835cf4025a74516a92df9501d093be0,
title = "Inevitability of phase-locking in a charge pump phase lock loop using deductive verification",
abstract = "Phase-locking in a charge pump (CP) phase lock loop (PLL) is said to be inevitable if all possible states of the CP PLL eventually converge to the equilibrium, where the input and output phases are in lock and the node voltages vanish. We verify this property for a CP PLL using deductive verification. We split this complex property into two sub-properties defined in two disjoint subsets of the state space. We deductively verify the first property using multiple Lyapunov certificates for hybrid systems, and use the Escape certificate for the verification of the second property. Construction of deductive certificates involves positivity check of polynomial inequalities (which is an NP-Hard problem), so we use the sound but incomplete Sum of Squares (SOS) relaxation algorithm to provide a numerical solution.",
keywords = "AMS circuits, Deductive verification, Escape certificate, Lyapunov certificate, SOS programming",
author = "{Ul Asad}, Hafiz and Jones, {Kevin D.}",
note = "Publisher Copyright: Copyright {\textcopyright} 2015 ACM.; 25th Great Lakes Symposium on VLSI, GLSVLSI 2015 ; Conference date: 20-05-2015 Through 22-05-2015",
year = "2015",
month = may,
day = "20",
doi = "10.1145/2742060.2742072",
language = "English",
series = "Proceedings of the ACM Great Lakes Symposium on VLSI, GLSVLSI",
publisher = "Association for Computing Machinery (ACM)",
pages = "295--300",
booktitle = "GLSVLSI 2015 - 25th 2015 Great Lakes Symposium on VLSI",
address = "United States",
}