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arXiv · 1803.05640

Optimal Weight Allocation of Dynamic Distribution Networks and Positive Semi-definiteness of Signed Laplacians

Jieqiang Wei·Alexander Johansson·Henrik Sandberg·Karl H. Johansson·Jie Chen
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Abstract

In this paper, we consider the robustness of a basic model of a dynamical distribution network. In the first problem, i.e., optimal weight allocation, we minimize the H-inf- norm of the dynamical distribution network subject to allocation of the weights on the edges. It is shown that this optimization problem can be formulated as a semi-definite program. Next we consider the semi-definiteness of the weighted graph Laplacian matrix with negative weights on the edges. A necessary and sufficient condition, using the effective resistance matrix, is established to guarantee the positive semi-definiteness of the Laplacian matrix. Furthermore, the bounded real lemma is derived for state-space symmetric systems.

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Jieqiang Wei, Alexander Johansson, Henrik Sandberg, Karl H. Johansson, Jie Chen. 2018-03-15. Optimal Weight Allocation of Dynamic Distribution Networks and Positive Semi-definiteness of Signed Laplacians. https://arxiv.org/abs/1803.05640

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