A resistance-based approach to consensus algorithm performance analysis

Abstract-We study the well known linear consensus algorithm by means of a LQ-type performance cost. We want to understand how the communication topology influences this algorithm. In order to do this, we recall the analogy between Markov Chains and electrical resistive networks. By exploiting this analogy, we are able to rewrite the performance cost as the average effective resistance on a suitable network. We use this result to show that if the communication graph fulfills some local properties, then its behavior can be approximated with that of a suitable grid, over which the behavior of the cost is known.

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Federica Garin, Enrico Lovisari, Sandro Zampieri
• Keywords: CDC 2010, Control Systems, Linear Consensus Algorithm, LQ-type Performance Cost, Performance Cost