ABSTRACT This paper provides an analysis of uncertain discrete-time negative imaginary and positive real systems with state-space symmetry. First, a necessary and sufficient condition is provided for a minimal state-space symmetric system to be discrete-time positive real or discrete-time negative imaginary. Then, based on the discrete-time symmetric negative imaginary and positive real lemmas, bounds on symmetrically structured perturbations that maintain the negative imaginariness and positive realness of a discrete-time state-space symmetric system are derived. Finally, an RL network example is provided to illustrate the main results of the paper.

中文翻译：

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不确定离散时间状态空间对称系统的正实性和负虚性

摘要 本文提供了具有状态空间对称性的不确定离散时间负虚和正实系统的分析。首先，给出了一个最小状态空间对称系统是离散时间正实数或离散时间负虚数的充要条件。然后，基于离散时间对称负虚数和正实数引理，导出了保持离散时间状态空间对称系统的负虚数和正实数的对称结构扰动的边界。最后，提供了一个 RL 网络示例来说明论文的主要结果。