This paper introduces the class of Time-Domain Input–Output Negative Imaginary () systems. The new definition unifies the class of the existing Negative Imaginary (NI) systems, including those that have imaginary-axis poles. A new dynamic dissipative framework is proposed to define and characterise the systems. This framework does not impose any conditions on the system, such as asymptotic stability, minimality, full normal rank constraint, etc., which are commonly used in the NI literature. Dynamic dissipativity of systems also leads to an LMI-based state-space characterisation, which can be conveniently used to classify the strict/non-strict properties of a given system. This paper also reveals the connections amongst the NI theory, dynamic dissipativity and classical dissipativity. Subsequently, a frequency-domain dissipative supply rate is also proposed to describe the whole class of systems, which is defined with respect to a shifted imaginary axis to capture particularly the systems having poles on the imaginary axis. This trick overcomes the limitation of earlier frequency-domain dissipative frameworks to capture systems with imaginary-axis poles. Finally, the derived results are specialised for the Time-Domain Output (Strictly) Negative Imaginary subclass since such systems exhibit useful closed-loop stability properties when connected in a positive feedback loop. Several illustrative numerical examples are provided to make the results intuitive and useful.

中文翻译：

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时域输入输出负虚数系​​统的动态耗散特性

本文介绍了一类时域输入输出负虚数 () 系统。新定义统一了现有负虚数 (NI) 系统的类别，包括具有虚轴极点的系统。提出了一种新的动态耗散框架来定义和表征系统。该框架没有对系统强加任何条件，如NI文献中常用的渐近稳定性、极小性、完全正态秩约束等。系统的动态耗散性还导致基于 LMI 的状态空间表征，可以方便地用于对给定系统的严格/非严格属性进行分类。本文还揭示了 NI 理论、动态耗散性和经典耗散性之间的联系。随后，还提出了频域耗散供给率来描述整类系统，其相对于移位的虚轴来定义，以特别捕获在虚轴上具有极点的系统。该技巧克服了早期频域耗散框架捕获具有虚轴极点的系统的限制。最后，导出的结果专门针对时域输出（严格）负虚数子类，因为此类系统在连接到正反馈环路时表现出有用的闭环稳定性特性。提供了几个说明性的数值示例，使结果直观且有用。