Time-domain output negative imaginary systems and its connection to dynamic dissipativity
Time-domain output negative imaginary systems and its connection to dynamic dissipativity
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DOI：
10.1109/cdc42340.2020.9304292
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
P. Bhowmick;A. Lanzon
中科院分区：
文献类型：
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作者：
P. Bhowmick;A. Lanzon
本文引入了时域输出（不一定严格）负虚系统的概念，它包含了负虚系统类的所有现有子集（不仅是稳定子集）。本文建立了一个时域动态耗散框架来描述全类输出负虚系统（即包括虚轴上有极点的系统）。这种动态耗散框架还导致了基于LTI的状态空间表征，可以方便地用于测试给定LTI系统的输出负虚数特性。进一步证明了对于时域输出负虚系统，所提出的动态耗散框架等价于该类系统关于供给率$w(u,\dot {\bar {y}})$的经典耗散性质。有趣的是，时域输出严格负虚系统的类别现在捕获了不一定稳定的系统-发现大多数在原点具有简单极点的SISO， LTI传递函数满足这一性质。为了更好地说明，文中还提供了数值例子。
This paper introduces the notion of time-domain output (not necessarily strictly) negative imaginary systems that encompasses all the existing (not only stable) subsets of the negative imaginary systems class. A time-domain dynamic dissipative framework is developed in this paper to describe the full class of output negative imaginary systems (i.e. including systems having poles on the imaginary axis). This dynamic dissipative framework also leads to an LMI-based state-space characterization which can be conveniently used to test the output negative imaginary property of a given LTI system. It is further established that for time-domain output negative imaginary systems, the proposed dynamic dissipative framework is equivalent to the classical dissipative property of this class of systems with respect to the supply rate $w(u,\dot {\bar {y}})$. Interestingly, the class of time-domain output strictly negative imaginary systems now captures systems that are not necessarily stable – it is found that the majority of the SISO, LTI transfer functions with a simple pole at the origin satisfy this property. Numerical examples are provided throughout the paper for better illustration.