Title :
On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms
Author :
Olshevsky, Alex ; Tsitsiklis, John N.
Author_Institution :
Lab. for Inf. & Decision Syst., Massachusetts Inst. of Technol., Cambridge, MA
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 . We also briefly discuss sufficient conditions for the existence of such a Lyapunov function.
Keywords :
Lyapunov matrix equations; multi-agent systems; consensus algorithms; linear agreement algorithms; quadratic Lyapunov functions; Communication networks; Convergence; Lyapunov method; Multiagent systems; Sufficient conditions; Consensus algorithms; Lyapunov theory; multi-agent systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2008.2007878
