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

TL;DR

This paper proves that leader-following exponential consensus can be achieved in linear multi-agent systems over switching networks, even with exponentially unstable system matrices, expanding the applicability beyond marginally stable systems.

Contribution

It demonstrates that exponential consensus is possible for unstable systems over jointly connected switching networks, and introduces output-based distributed observer design under these conditions.

Findings

Exponential consensus achievable for unstable systems.

Explicit characterization of instability degree.

Distributed observer design works for unstable leader systems.

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.