On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms
Alex Olshevsky, John N. Tsitsiklis
TL;DR
This paper proves that for a specific class of linear consensus algorithms, no quadratic Lyapunov function exists, highlighting limitations in stability analysis methods for these algorithms.
Contribution
It provides a concrete example demonstrating the nonexistence of quadratic Lyapunov functions for certain consensus algorithms and discusses conditions for their existence.
Findings
No quadratic Lyapunov function exists for the example provided.
Numerical verification confirmed the nonexistence.
Conditions for the existence of such functions are briefly discussed.
Abstract
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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Taxonomy
TopicsDistributed Control Multi-Agent Systems · Neural Networks Stability and Synchronization · Modular Robots and Swarm Intelligence