## Abstract

This paper investigates the distributed computation of the well-known linear matrix equation in the form of AXB = F, with the matrices A, B, X, and F of appropriate dimensions, over multiagent networks from an optimization perspective. In this paper, we consider the standard distributed matrix-information structures, where each agent of the considered multiagent network has access to one of the subblock matrices of A, B, and F To be specific, we first propose different decomposition methods to reformulate the matrix equations in standard structures as distributed constrained optimization problems by introducing substitutional variables; we show that the solutions of the reformulated distributed optimization problems are equivalent to least squares solutions to original matrix equations; and we design distributed continuous-time algorithms for the constrained optimization problems, even by using augmented matrices and a derivative feedback technique. Moreover, we prove the exponential convergence of the algorithms to a least squares solution to the matrix equation for any initial condition.

Original language | English |
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Article number | 8385114 |

Pages (from-to) | 1858-1873 |

Number of pages | 16 |

Journal | IEEE Transactions on Automatic Control |

Volume | 64 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2019 |

## Keywords

- Constrained convex optimization
- distributed computation
- least squares solution
- linear matrix equation
- substitutional decomposition