On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms
Alex Olshevsky, John N. Tsitsiklis · IEEE Transactions on Automatic Control · 2008
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 . We also briefly discuss sufficient conditions for the existence of such a Lyapunov function.