The communication network is usually susceptible to effective communication channel capacity variation and transmission imperfections, which renders the connection among networked agents unstable. Motivated by this fact, we assume that the communication graphs are Markovian randomly switching, because the Markovian chain process is commonly employed to describe the network subject to Rayleigh fading channel. Under such a communication connection assumption, this article investigates the globally leader‐following consensus control problem for grouped agents with nonlinear dynamics. Different nonlinear dynamics, including Lur'e and Lorenz‐type chaotic systems, are considered. By using the tools from the robust control theory, the conditions guaranteeing the globally leader‐following consensus are derived. Under such conditions, consensus control protocols can be designed solely based on the relative state information transmitted over the communication network, by solving some linear matrix inequalities. Then, we characterize the robustness of the controlled systems against the variation of the communication graphs with the globally leader‐following consensus performance region. It is theoretically shown that the networked nonlinear systems under the proposed controller yield unbounded and connected robust performance regions. Finally, the theoretical results are verified by conducting numerical simulations on networks consisting of Chua's oscillators and Lü systems.

中文翻译：

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基于性能区域的非线性多主体系统领导者遵循共识方法

通信网络通常容易受到有效的通信信道容量变化和传输缺陷的影响，这使得联网的代理之间的连接不稳定。出于这一事实，我们假定通信图是马尔可夫随机切换的，因为通常使用马尔可夫链过程来描述受瑞利衰落信道影响的网络。在这种通信连接假设下，本文研究了具有非线性动力学的分组代理的全局领导者遵循共识控制问题。考虑了不同的非线性动力学，包括Lur'e和Lorenz型混沌系统。通过使用鲁棒控制理论中的工具，可以确保全球范围内的条件得出领导者以下共识。在这种情况下，可以通过解决一些线性矩阵不等式，仅基于通过通信网络传输的相对状态信息来设计共识控制协议。然后，我们针对全局领导者遵循共识绩效区域的通信图变化，描述了受控系统的鲁棒性。从理论上可以看出，所提出的控制器下的网络非线性系统产生了无界和连通的鲁棒性能区域。最后，通过对由蔡氏振荡器和Lü系统组成的网络进行数值模拟，验证了理论结果。