State convergence is essential in many scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, computational game theory, multi-agent learning over networks. In this paper, we study for the first time the state convergence problem in uncertain linear systems. Preliminarily, we characterize state convergence in linear systems via equivalent linear matrix inequalities. In the presence of uncertainty, we complement the canonical definition of (weak) convergence with a stronger notion of convergence, which requires the existence of a common kernel among the generator matrices of the difference/differential inclusion (strong convergence). We investigate under which conditions the two definitions are equivalent. Then, we characterize strong and weak convergence via Lyapunov arguments, (linear) matrix inequalities and separability of the eigenvalues of the generator matrices. Finally, we show that, unlike asymptotic stability, state convergence lacks of duality.

状态收敛在许多科学领域都是必不可少的，例如多智能体共识/分歧，分布式优化，计算博弈论，网络上的多智能体学习。在本文中，我们首次研究了不确定线性系统的状态收敛问题。初步，我们通过等效线性矩阵不等式表征线性系统中的状态收敛。在存在不确定性的情况下，我们用更强的收敛概念来补充（弱）收敛的规范定义，这要求差异/微分包含（强收敛）的生成器矩阵之间存在一个公共核。我们研究在什么条件下两个定义是等效的。然后，我们通过李雅普诺夫论证来描述强收敛和弱收敛，（线性）矩阵不等式和生成器矩阵特征值的可分离性。最后，我们证明，与渐近稳定性不同，状态收敛缺乏对偶性。