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Title: Localized Stability Analysis and Design of Symmetric Spatially Distributed Systems over Sparse Proximity Graphs
The focus of this paper is on the finite or infinite dimensional class of spatially distributed linear systems with Hermitian and sparse state matrices. We show that exponential stability of this class of systems can be inferred in a decentralized and spatially localized manner, which is practically relevant to many real-world applications (e.g., systems with spatially discredited PDE models). Then, we obtain several sufficient conditions that allow us to adjust strength of existing couplings in a network in order to sparsify or grow a network, while ensuring global stability. Our proposed necessary and sufficient stability certificates are independent of the dimension of the entire system. Moreover, they only require localized knowledge about the state matrix of the system, which makes these verifiable conditions desirable for design of robust spatially distributed linear systems against subsystem failure and replacement.  more » « less
Award ID(s):
1412413
PAR ID:
10131737
Author(s) / Creator(s):
;
Date Published:
Journal Name:
23rd International Symposium on Mathematical Theory of Networks and Systems
Page Range / eLocation ID:
185 - 188
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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