Leader-following Consensus over Jointly Connected Switching Networks is Achievable for Exponentially Unstable Linear Systems
This solves a long-standing challenge in control theory for multi-agent systems, enabling applications like robotics and autonomous vehicles with unstable dynamics, though it is a foundational breakthrough rather than incremental.
The paper tackles the leader-following consensus problem for general linear multi-agent systems over switching networks, showing that exponential consensus is achievable even when the system matrix is exponentially unstable, which was previously limited to marginally stable systems.
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.