Finite-time general function consensus for multi-agent systems over signed digraphs

This paper solves the finite-time consensus problem for discrete time multi-agent systems (MASs) where agents update their values via linear iteration and the interactions between them are described by signed digraphs. A sufficient condition is presented that the agents can reach consensus on any given linear function of multiple initial signals in finite time, i.e., there exists an eventually positive Laplacianbased matrix associated with the underlying graph. We prove that the linear iterative framework ratio consensus developed for unsigned graphs in the literature can be extended to the computation for signed graphs with appropriate modifications. Our method weakens the limitation of the iterative framework on the marginal Schur stability of the weight matrix without increasing the computational complexity. Reaching average consensus on unsigned graphs as in the literature is regarded as a special case of our algorithm. Two illustrative examples are presented to demonstrate the correctness of the proposed results.& COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

This paper solves the finite-time consensus problem for discrete time multi-agent systems (MASs) with agents updating their values via linear iteration and interactions described by signed digraphs. A sufficient condition is presented for agents to reach consensus on any given linear function of multiple initial signals in finite time. The method extends the existing linear iterative framework for unsigned graphs to computation for signed graphs with appropriate modifications.