We examine the H2\mathcal {H}_2 norm of matrix-weighted leader-follower consensus on series-parallel networks. By using an extension of electrical network theory on matrix-valued resistances, voltages, and currents, we show that the computation of the H2{\mathcal {H}_2} norm can be performed efficiently by decomposing the network into atomic elements and composition rules. Finally, we examine the problem of efficiently adapting the matrix-valued edge weights to optimize the H2{\mathcal {H}_2} norm of the network.

中文翻译：

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${\mathcal {H}_2}$串并网络的性能：组合视角


我们研究了串联并行网络上矩阵加权领导者-跟随者共识的 H2\mathcal {H}_2 范数。通过使用电气网络理论对矩阵值电阻、电压和电流的扩展，我们表明可以通过将网络分解为原子元素和组成规则来有效地计算 H2{\mathcal {H}_2} 范数。最后，我们研究有效调整矩阵值边权重以优化网络的 H2{\mathcal {H}_2} 范数的问题。