${\mathcal{H}}_2$ performance of series-parallel networks: A compositional perspective

Abstract

We examine the ${\mathcal{H}}_2$ 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 ${\mathcal{H}}_2$ norm can be performed efficiently by decomposing the network into atomic elements and composition rules. Lastly, we examine the problem of efficiently adapting the matrix-valued edge weights to optimize the ${\mathcal{H}}_2$ norm of the network.

Provisionally accepted to the IEEE Transactions on Automatic Control. arXiv admin note: substantial text overlap with arXiv:1903.05325

References in corpus (2)

• Novel type of phase transition in a system of self-driven particles
• Efficient Computation of H2 Performance on Series-Parallel Networks

Cited by in corpus (3)

• Performance and design of consensus on matrix-weighted and time scaled graphs
• ${\mathcal{H}}_{\infty }$ Network Optimization for Edge Consensus
• Self-Tuning Network Control Architectures