Performance and Design of Consensus on Matrix-Weighted and Time-Scaled Graphs

Abstract

In this article, we consider the ${\mathcal {H}_2}$ -norm of networked systems with multi-time-scale consensus dynamics and vector-valued agent states. This allows us to explore how measurement and process noise affect consensus on matrix-weighted graphs by examining edge-state consensus. In particular, we highlight an interesting case where the influences of the weighting and scaling on the ${\mathcal {H}_2}$ -norm can be separated in the design problem. We then consider optimization algorithms for updating the time-scale parameters and matrix weights in order to minimize network response to injected noise. Finally, we present an application to formation control for multivehicle systems.