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：一般线性多智能体系统在联合连通切换网络下的领导者-跟随一致性问题长期以来一直是一个具有挑战性的难题，且该问题的可解性仅限于系统矩阵为临界稳定的线性多智能体系统类别。这一条件具有严格限制性，因其甚至排除了最常用的双积分器系统。本文通过证明在联合连通切换网络下，即使系统矩阵呈指数不稳定，一般线性多智能体系统仍可实现领导者-跟随指数一致性，从而取得了突破性进展。不稳定程度可通过切换图联合连通条件中产生的两个关键量值进行显式刻画。通过利用对偶性，我们进一步证明，即使系统矩阵呈指数不稳定，一般领导者系统的基于输出的分布式观测器设计问题在联合连通切换网络下仍是可解的。这与现有分布式观测器形成鲜明对比，后者均依赖于领导者系统为临界稳定的假设。