Leader-following Consensus over Jointly Connected Switching Networks is Achievable for Exponentially Unstable Linear Systems

2026-02-08

AI Summary

This study addresses leader-following consensus for linear multi-agent systems with exponentially unstable system matrices under jointly connected switching networks. Moving beyond the conventional requirement of marginal stability for the system matrix, the work proposes a distributed output-feedback observer design method grounded in graph-theoretic joint connectivity analysis, duality principles, and linear system stability theory. It is rigorously established—for the first time—that exponential leader-following consensus can still be achieved even when the system matrix is exponentially unstable, provided the communication topology remains jointly connected over time. The solvability of the proposed distributed observer is also verified, thereby significantly broadening the applicability of existing consensus theory to more general and challenging system dynamics.

Technology Category

• Multiagent Systems: Multiagent Systems under Uncertainty
• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The leader-following consensus problem for general linear multi-agent systems over jointly connected switching networks has been a challenging problem and the solvability of the problem has been limited to the class of linear multi-agent systems whose system matrix is marginally stable. This condition is restrictive since it even excludes the most commonly used double-integrator system. This paper presents a breakthrough by demonstrating that leader-following exponential consensus is achievable for general linear multi-agent systems over jointly connected switching networks, even when the system matrix is exponentially unstable. The degree of instability can be explicitly characterized by two key quantities that arise from the jointly connected condition on a switching graph. By exploiting duality, we further show that the output-based distributed observer design problem for a general leader system is solvable over jointly connected switching networks, even when the system matrix is exponentially unstable. This is also in sharp contrast to the existing distributed observers, which rely on the assumption that the leader system is marginally stable.

Problem

• leader-following consensus
• exponentially unstable systems
• jointly connected switching networks
• multi-agent systems
• distributed observer

Innovation

• leader-following consensus
• exponentially unstable systems
• jointly connected switching networks
• distributed observer
• duality