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Distributed solver for linear matrix inequalities: an optimization perspective

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Abstract

In this paper, we develop a distributed solver for a group of strict (non-strict) linear matrix inequalities over a multi-agent network, where each agent only knows one inequality, and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions. The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints. Then, by the primal–dual methods, a distributed algorithm is proposed with the help of projection operators and derivative feedback. Finally, the convergence of the algorithm is analyzed, followed by illustrative simulations.

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Acknowledgements

This work was supported by the Shanghai Municipal Science and Technology Major Project (No. 2021SHZDZX0100) and the National Natural Science Foundation of China (Nos. 61733018, 62073035).

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Correspondence to Wen Deng.

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Li, W., Deng, W., Zeng, X. et al. Distributed solver for linear matrix inequalities: an optimization perspective. Control Theory Technol. 19, 507–515 (2021). https://doi.org/10.1007/s11768-021-00061-z

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  • DOI: https://doi.org/10.1007/s11768-021-00061-z

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