Localized Stability Certificates for Spatially Distributed Systems over Sparse Proximity Graphs
Localized Stability Certificates for Spatially Distributed Systems over Sparse Proximity Graphs
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DOI：
10.1137/19m1298834
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
N. Motee;Qiyu Sun
中科院分区：
文献类型：
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作者：
N. Motee;Qiyu Sun
- 我们提出了局部化条件来检查空间分布线性系统的指数稳定性。本文重点讨论的系统，其耦合结构的定义使用测地线的邻近通信图。我们重新制定的指数稳定性条件的形式的可行性条件，是服从本地化的实现。使用有限截断技术，我们得到分散的必要和充分的稳定性证明。为了保证全局稳定性，它足以证明图覆盖上的局部化条件，其中验证每个局部化证书的计算复杂度与网络大小无关。然后，我们分析具有对称状态空间矩阵的线性网络。几个鲁棒性条件对局部矩阵扰动是有用的，以分散的方式调整网络参数，同时确保全局稳定性。
—We propose localized conditions to check exponential stability of spatially distributed linear systems. This paper focuses on systems whose coupling structures are defined using a geodesic on proximity communication graphs. We reformulate the exponential stability condition in the form of a feasibility condition that is amenable to localized implementations. Using finite truncation techniques, we obtain decentralized necessary and sufficient stability certificates. In order to guarantee global stability, it suffices to certify localized conditions over a graph covering, where the computational complexity of verifying each localized certificate is independent of network size. Then, we analyze linear networks with symmetric state-space matrices. Several robustness conditions against local matrix perturbations are obtained that are useful for tuning network parameters in a decentralized manner while ensuring global stability.