Abstract
This paper is concerned with a consensus problem for large scale network systems. Our goal is to design the feedback gains of each system as a function of its degree in such a way that the rate of convergence takes its maximum. We propose a new criteria called normalized eigenvalue variance as the measure of the convergence speed of a large scale network with many agents. It permits an assessment of the convergence performance of homogeneous graphs. We demonstrate the design method of the agents' feedback gains minimizing the normalized eigenvalue variance.
