On the Role of Interconnection Directionality in the Quadratic Performance of Double-Integrator Networks

This article provides a quantitative and qualitative evaluation of the role of interconnection directionality in a general class of quadratic performance metrics for double-integrator networks. We first develop an analysis framework that can be used to evaluate the quadratic performance metrics of networks defined over a general class of directed graphs. A comparison between systems whose directed graph Laplacians are normal and their undirected counterparts unveils an interplay between the interconnection directionality and the control strategy that determines network performance. We show that directionality can significantly degrade performance; however, well-designed feedback can exploit directionality to mitigate this degradation or even improve performance.