Properties of positive feedback interconnected negative imaginary systems
Properties of positive feedback interconnected negative imaginary systems
复制标题
DOI：
10.23919/ascc56756.2022.9828277
复制
发表时间：
2022-05
期刊：
影响因子：
--
通讯作者：
P. Bhowmick;Hsueh-Ju Chen;A. Lanzon
中科院分区：
文献类型：
--
作者：
P. Bhowmick;Hsueh-Ju Chen;A. Lanzon
本文解决了为两个负虚数 (NI) 系统的正反馈互连找到一组“当且仅当”标准以保留 NI 属性的问题。首先，我们推导了 NI 系统的状态空间表征，该系统不施加极小性限制。然后，提供了两个更重要的先决技术引理来证明本文的主要结果，即处理互连系统属性。在一些技术假设下，本文表明，两个 NI 系统在 s = 0 时具有可能的极点的正反馈互连保留了 NI 属性。随后，当 NI 系统在 s = 0 处没有任何极点时，结果会被专门化，然后是 SNI 系统。所提出的结果在大型车辆排的分散控制中具有潜在的应用。此外，结果可用于简化复杂的物理网络以及物理网络分析和综合。
This paper addresses the problem of finding a set of ‘if and only if’ criteria for a positive feedback interconnection of two Negative Imaginary (NI) systems to retain the NI property. First, we have derived a state-space characterisation for NI systems that does not impose the minimality restriction. Then, two more essential pre-requisite technical lemmas are provided to prove the main results of this paper, which deal with interconnected system properties. Under some technical assumptions, the paper shows that a positive feedback interconnection of two NI systems with possible pole(s) at s = 0 preserves the NI property. Subsequently, the result is specialised when the NI systems do not have any pole(s) at s = 0 and then to SNI systems. The proposed results have potential applications in decentralised control of large vehicle platoons. Furthermore, the results may be utilised in simplifying complex physical networks and in physical network analysis and synthesis.