On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms

Alex Olshevsky; John N. Tsitsiklis

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On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms

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arxiv 0706.2876 v2 pith:7SXMTNBU submitted 2007-06-19 math.OC

Alex Olshevsky , John N. Tsitsiklis This is my paper · ORCID

classification math.OC

keywords lyapunovalgorithmsconsensusfunctionquadraticagreementbeenbriefly

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We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [5]. We also briefly discuss sufficient conditions for the existence of such a Lyapunov function.

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