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.

翻译：针对一般线性多智能体系统在联合切换网络上的领导者-跟随者一致性问题，该问题的可解性此前仅限于系统矩阵为临界稳定的一类线性多智能体系统。由于该条件甚至排除了最常用的双积分器系统，因此存在较大局限性。本文通过证明即使系统矩阵呈指数不稳定时，一般线性多智能体系统在联合切换网络上仍可实现指数型领导者-跟随者一致，取得了突破性进展。该不稳定程度可通过切换图联合连通条件衍生的两个关键量进行显式刻画。进一步利用对偶性，我们证明即使系统矩阵呈指数不稳定时，一般领导者系统在联合切换网络上的输出型分布式观测器设计问题仍可解。这与现有依赖领导者系统临界稳定假设的分布式观测器形成鲜明对比。