Characterization of ℋ-ℋ- index for linear time-varying systems
Characterization of ℋ-ℋ- index for linear time-varying systems
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DOI：
10.1016/j.automatica.2013.02.001
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
Xiaobo Li;H. Liu
中科院分区：
文献类型：
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作者：
Xiaobo Li;H. Liu
在故障检测中对指数的兴趣越来越大，导致了时域研究的一些最新发展。本文首先给出了线性时变系统在有限时域内存在λ-指标的一个充要条件。它表明，的可行性的指标，这是给定的，当该指标是大于一个预定义的值，是等价于存在一个特定的后向微分Riccati方程的约束。作为一种特殊情况，讨论了平方系统。相应的结果被推广到具有未知初始条件的系统与修改的定义的指数。通过变换，导出了加权指标在不同时刻强调信号作用的条件。并与著名的有界真实的引理进行了比较。与线性时不变（LTI）的情况下的连接进行了讨论。最后，给出了一些例子来说明主要结果.
The increasing interest in ℋ−index in fault detection has led to some recent development in time domain investigation. This paper at first presents a necessary and sufficient condition of the ℋ−index in finite time horizon for linear time-varying systems. It is shown that the feasibility of the ℋ−index, which is given when the ℋ−index is greater than a predefined value, is equivalent to the existence of a certain backward differential Riccati equation under a constraint. The square system as a special case is discussed. The corresponding results are extended to systems with unknown initial condition with a modified definition of the ℋ−index. The condition for weighted index to emphasize the signal effect at different time instant is also derived by transformation. The result is also compared with the famous bounded real lemma. The connection with the linear time-invariant (LTI) case is also discussed. Finally, examples are given to illustrate the main results.