A robust output feedback consensus problem for networked identical nonlinear negative-imaginary (NI) systems is investigated in this paper. Output consensus is achieved by applying identical linear output strictly negative-imaginary (OSNI) controllers to all the nonlinear NI plants in positive feedback through the network topology. First, we extend the definition of nonlinear NI systems from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and also extend the definition of OSNI systems to nonlinear scenarios. Asymptotic stability is proved for the closed-loop interconnection of a nonlinear NI system and a nonlinear OSNI system under reasonable assumptions. Then, an NI property and an OSNI-like property are proved for networked identical nonlinear NI systems and networked identical linear OSNI systems, respectively. Output feedback consensus is proved for a network of identical nonlinear NI plants by investigating the stability of its closed-loop interconnection with a network of linear OSNI controllers. This closed-loop interconnection is proposed as a protocol to deal with the output consensus problem for networked identical nonlinear NI systems and is robust against uncertainty in the individual system's model.

中文翻译：

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网络相同非线性负虚系统的鲁棒输出反馈共识

本文研究了网络相同非线性负虚 (NI) 系统的鲁棒输出反馈一致性问题。输出一致性是通过将相同的线性输出严格负虚数 (OSNI) 控制器应用于所有非线性 NI 设备以通过网络拓扑进行正反馈来实现的。首先，我们将非线性 NI 系统的定义从单输入单输出 (SISO) 系统扩展到多输入多输出 (MIMO) 系统，并将 OSNI 系统的定义扩展到非线性场景。在合理的假设下，证明了非线性 NI 系统和非线性 OSNI 系统的闭环互连的渐近稳定性。然后，证明了网络相同非线性NI系统和网络相同线性OSNI系统的NI性质和类OSNI性质，分别。通过研究其与线性 OSNI 控制器网络的闭环互连的稳定性，证明了相同非线性 NI 设备网络的输出反馈一致性。这种闭环互连被提议作为一种协议来处理联网的相同非线性 NI 系统的输出一致性问题，并且对单个系统模型中的不确定性具有鲁棒性。