Distributed Positive Consensus Protocol Design for Leader-Following Multi-Agent Systems under Fixed and MDMDT Switching Topologies
Shuo Li, Yongqi Jia, Zhengrong Xiang · Journal of Circuits Systems and Computers · 2025
In this paper, the leader-following positive consensus (LFPC) issue of multi-agent systems (MASs) is systematically addressed. The study considers both fixed topology and mode-dependent minimum dwell time (MDMDT) switching topology. First, focusing on fixed topology, the study begins by utilizing positive systems theory to derive a condition that is both necessary and sufficient to ascertain that the specified closed-loop system qualifies as a positive system. Next, based on the constructed consensus error system and employing an appropriate linear co-positive Lyapunov function, the paper presents a sufficient condition for achieving LFPC. Consequently, the application of the matrix decomposition method to matrix K is executed, and a valid distributed consensus protocol design scheme is introduced in a solvable linear programming (LP) format to achieve LFPC. In the following section, the paper addresses the MDMDT switching topology. It presents a condition that is both necessary and sufficient for verifying that the closed-loop system operates as a positive system under MDMDT switching topology. Utilizing the constructed consensus error system and the discretized linear copositive Lyapunov function (DLCLF) method, the paper puts forward a sufficient condition for LFPC under this switching topology. Lastly, by utilizing matrix decomposition techniques to matrix [Formula: see text], a valid distributed consensus protocol design scheme is introduced in a mode-dependent piece-wise solvable LP format to ensure LFPC in the context of the MDMDT switching topology. Unlike general LMI-based approaches, the proposed LP-based distributed protocol scheme offers a simpler form of consensus conditions and lower computational complexity, making it easier to manage large-scale MASs. Ultimately, two examples are presented in the context of communication networks to demonstrate the effectiveness of the designed distributed protocol.