This paper examines the ${\mathcal{H}}_{\infty }$ performance problem of the edge agreement protocol for networks of agents operating on independent time scales, connected by weighted edges, and corrupted by exogenous disturbances. ${\mathcal{H}}_{\infty }$-norm expressions and bounds are computed that are then used to derive new insights on network performance in terms of the effect of time scales and edge weights on disturbance rejection. We use our bounds to formulate a convex optimization problem for time scale and edge weight selection. Numerical examples are given to illustrate the applicability of the derived ${\mathcal{H}}_{\infty }$-norm bound expressions, and the optimization paradigm is illustrated via a formation control example involving non-homogeneous agents.

本文考察了 ${\mathcal{H}}_{\infty }$ 边缘协议协议在独立时间尺度上运行的代理网络的性能问题，通过加权边缘连接，并被外生干扰破坏。 ${\mathcal{H}}_{\infty }$- 范数表达式和界限被计算出来，然后用于根据时间尺度和边缘权重对干扰抑制的影响得出对网络性能的新见解。我们使用我们的边界来为时间尺度和边缘权重选择制定一个凸优化问题。给出了数值例子来说明导出的适用性${\mathcal{H}}_{\infty }$-范数边界表达式，并且优化范例通过涉及非同质代理的编队控制示例进行说明。