In this paper, we study consensus problem in a discrete-time multi-agent system with uncertain topologies and random delays governed by a Markov chain. The communication topology is assumed to be directed but interrupted by system uncertainties. Furthermore, the system delays are modeled by a Markov chain. We first use a reduced-order system featuring the error dynamics to transform the consensus problem of the original one into the stabilization of the error dynamic system. By using the linear matrix inequality method and the stability theory in stochastic systems with time-delay, several sufficient conditions are established for the mean square stability of the error dynamics which guarantees consensus. By redesigning its adjacency matrices, we develop a switching control scheme which is delay-dependent. Finally, simulation results are worked out to illustrate the theoretical results.

中文翻译：

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由马尔可夫链控制的具有不确定拓扑和随机延迟的离散多主体系统的共识

在本文中，我们研究了具有不确定拓扑和由Markov链控制的随机时滞的离散时间多主体系统的共识问题。假定通信拓扑是有方向的，但由于系统不确定性而中断。此外，系统延迟是通过马尔可夫链建模的。我们首先使用具有误差动态特性的降阶系统将原始误差系统的共识问题转化为误差动态系统的稳定化。通过使用线性矩阵不等式方法和具有时滞的随机系统的稳定性理论，为误差动力学的均方稳定性建立了几个充分的条件，从而保证了一致。通过重新设计其邻接矩阵，我们开发了依赖于延迟的切换控制方案。最后，