文章研究了马氏切换拓扑下多自主体系统的鲁棒 $H_{\mathrm{\infty }}$ 领导 跟踪一致性问题. 由于通讯环境中难以预知的变化, 自主体之间的通讯连接可能具 有随机的不确定成分, 文章用伯努利分布序列来描述这种随机不确定性. 同时, 在很多实际系统中, 想精准获得马氏跳变过程的转移率矩阵中的元素是不容易的, 或者获取成本很高, 因此文章中马氏切换拓扑的转移率是假定为部分未知的. 通过使用随机理论和 $H_{\mathrm{\infty }}$ 控制技术, 得到了用线性矩阵不等式表示的充分条件, 使得所有的跟随者都将在均方意义下渐近跟踪领导者. 最后, 通过数值仿真验证了理论结果.

This paper investigates the robust~$H_{\mathrm{\infty }}$ leader-following consensus problem for multi-agent systems over Markovian switching topologies. Because of unpredictable changes of the communication environment, uncertainties of communication links may randomly occur among the agents, which are described by the Bernoulli distributed sequence. Moreover, because it is uneasy or costly to obtain the precise elements in the transition rate matrix of a Markovian jump process in many practical systems, the transition rates in the Markovian switching topologies are assumed to be partially unknown. By utilising the stochastic theory and~$H_{\mathrm{\infty }}$ control technique, sufficient conditions in terms of linear matrix inequalities are derived, under which all the followers will asymptotically track with the leader in the mean square sense. Finally, a numerical example is provided to demonstrate the validity of the theoretical results.