Output strictly negative imaginary systems and its connections to dissipativity theory
Output strictly negative imaginary systems and its connections to dissipativity theory
复制标题
DOI：
10.1109/cdc40024.2019.9030016
复制
发表时间：
2019-07
期刊：
影响因子：
--
通讯作者：
P. Bhowmick;A. Lanzon
中科院分区：
文献类型：
--
作者：
P. Bhowmick;A. Lanzon
本文概括了输出严格负虚数系统的概念，并提供了频域和时域的完整表征。该论文还揭示了负虚数理论与耗散性之间缺失的联系。引入新的时域供给率来表征输出严格负虚数系统的类别，该系统由系统的输入、系统辅助输出的导数和实参数 δ > 0 组成。此外，除了输出严格负虚数系统之外，所有稳定的负虚数系统对于 δ = 0 的相同供给率而言都是耗散的。在输出严格负虚数系统属性和此类系统的时域耗散性之间也建立了关于所建议的供应率和特定正定存储函数的等价性。研究了几个数值例子来阐明理论发展的本质。
This paper generalises the notion of output strictly negative imaginary systems and provides a complete characterisation both in frequency domain and time domain. The paper also reveals the missing link between the negative imaginary theory and dissipativity. A new time domain supply rate is introduced to characterise the class of output strictly negative imaginary systems that consists of input to the system, the derivative of an auxiliary output of the system and a real parameter δ > 0. Further, in addition to the output strictly negative imaginary systems, all stable negative imaginary systems are shown to be dissipative with respect to the same supply rate with δ =0. An equivalence is also established between the output strictly negative imaginary systems property and time domain dissipativity of this class of systems with respect to the proposed supply rate and a specific positive definite storage function. Several numerical examples are studied to elucidate the essence of the theoretical developments.