In this paper, we present necessary and sufficient conditions under which a linear time-invariant (LTI) system is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show that a minimal LTI strictly proper system can be rendered NI using full state feedback if and only if it can be output transformed into a system, which has relative degree less than or equal to two and is weakly minimum phase. We also considered the problems of state feedback equivalence to output strictly negative imaginary systems and strongly strict negative imaginary systems. Then we apply the NI state feedback equivalence result to robustly stabilize an uncertain system with strictly negative imaginary uncertainty. An example is provided to illustrate the proposed results, for the purpose of stabilizing an uncertain system.

中文翻译：

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负虚系统状态反馈等价的充要条件

在本文中，我们提出了线性时不变 (LTI) 系统是等效于负虚数 (NI) 系统的状态反馈的充分必要条件。更准确地说，我们表明，当且仅当它可以输出转换为相对度小于或等于 2 且弱最小相位的系统时，可以使用全状态反馈将最小 LTI 严格正确系统呈现为 NI。我们还考虑了输出严格负虚系统和强严格负虚系统的状态反馈等价问题。然后我们应用 NI 状态反馈等效结果来稳健地稳定具有严格负虚不确定性的不确定系统。为了稳定不确定系统，提供了一个示例来说明所提出的结果。