Robustness and Leadership in Markov-switching Consensus Networks

2026-06-24

AI Summary

This study addresses consensus and leader–follower tracking problems for multi-agent systems under Markov-switching network topologies in the presence of stochastic disturbances. Within the framework of Markov jump linear systems, the authors combine stochastic process analysis with graph-theoretic methods to derive explicit covariance expressions for both individual and collective steady-state tracking errors. Notably, they extend robustness metrics and joint centrality concepts—originally defined for static graphs—to dynamically switching topologies, thereby uncovering how dual-topology switching mechanisms influence steady-state performance. Theoretical analysis and numerical simulations demonstrate that topology switching can either significantly enhance or degrade system robustness, offering quantitative insights for designing highly robust cooperative strategies in multi-agent networks.

Abstract

We investigate how time-varying interactions, modeled via a Markov switching graph (MSG), impact the robustness of noisy multi-agent dynamics in both continuous- and discrete-time settings. Our focus is on the steady-state performance of consensus and leader-follower tracking dynamics subject to stochastic noise. Using the framework of Markov jump linear systems (MJLS), we derive expressions for the steady-state covariance of each agent's deviation from consensus and tracking error, respectively, and use them to quantify individual and group performance as a function of the interaction graphs and the switching dynamics. We extend established notions of robustness, certainty indices, and joint centrality from static graphs to the MSG setting. To gain analytical insight, we specialize our results to systems switching between two topologies and characterize how switching influences performance. Numerical simulations further illustrate how switching topologies affects system robustness in both coordination tasks.

Problem

• Markov-switching graph
• multi-agent systems
• robustness
• consensus
• leader-follower tracking

Innovation

• Markov switching graph
• multi-agent consensus
• steady-state covariance
• robustness
• leader-follower tracking