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A small-gain approach for consensus of heterogeneous linear multi-agent systems
Hye Seung Hong1, Hyeon-Woo Na1, PooGyeon Park1
1Department of Electrical Engineering, POSTECH, 77, Cheongam-ro, Pohang, 37673, Gyeongsangbuk-do, the Republic of Korea.
ISA Transactions
|October 24, 2025
Summary
This study introduces a small-gain method for achieving consensus in heterogeneous linear multi-agent systems. The approach ensures all agents reach a common state by stabilizing system dynamics and reducing errors.
Area of Science:
- Control Theory
- Systems Engineering
- Networked Systems
Background:
- Consensus problems in multi-agent systems are crucial for coordinated behavior.
- Heterogeneous systems present unique challenges due to differing agent dynamics.
- Directed graph topologies complicate the analysis of information flow and stability.
Purpose of the Study:
- To develop a novel small-gain approach for achieving consensus in heterogeneous linear multi-agent systems.
- To analyze the system dynamics by decomposing them into null and error dynamics blocks.
- To establish a stabilizing condition for consensus under directed graph topologies.
Main Methods:
- Decomposition of the system into null dynamics and error dynamics blocks using Laplacian perspective.
- Analysis of the interconnectedness of these blocks, highlighting differences from homogeneous systems.
- Construction of a merged block to derive a stabilizing condition for consensus.
Main Results:
- A stabilizing condition is derived, ensuring agent states converge to the null dynamics state.
- Errors between agent states converge to zero over time.
- An iterative algorithm is proposed to determine a gain matrix with a loop gain index less than one for consensus.
Conclusions:
- The proposed small-gain approach effectively achieves consensus in heterogeneous linear multi-agent systems.
- The method is validated through illustrative and practical examples.
- The findings offer a robust framework for designing decentralized control strategies for complex systems.
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