Convergence Rate of Accelerated Average Consensus with Local Node Memory: Optimization and Analytic Solutions

Previous researches have shown that adding local memory can accelerate the consensus. It is natural to question what fastest rate achievable by $M$ -tap acceleration, and are corresponding control parameters. This paper introduces a set of effective previously unused techniques analyze convergence accelerated consensus with nodes design protocols. These techniques, including Kharitonov stability theorem, Routh criterion robust margin, led following new results: 1) direct link between parameters; 2) explicit formulas optimal parameters for notation="LaTeX">$M \leq 2$ on given graph; 3) analytic worst-case \geq 1$ uncertain graphs. We show acceleration notation="LaTeX">$M=1$ provides in sense performance. Several numerical examples demonstrate validity performance theoretical results.