IEEE Transactions on Automatic Control, Vol.53, No.11, 2642-2645, 2008
On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms
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 [6]. We also briefly discuss sufficient conditions for the existence of such a Lyapunov function.