L1 gain analysis of linear positive systems and its application
L1 gain analysis of linear positive systems and its application
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DOI：
10.1109/cdc.2011.6160692
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
Y. Ebihara;D. Peaucelle;D. Arzelier
中科院分区：
文献类型：
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作者：
Y. Ebihara;D. Peaucelle;D. Arzelier
本文主要研究线性定常连续时间正系统的L1增益分析问题。一个正系统的特征在于它的输出对于任何非负输入总是非负的强性质。由于这一特性，很自然地可以用输入和输出信号的L1增益（即L1诱导范数）来估计正系统的大小。与标准的L1增益相比，在本文中，我们感兴趣的L1增益与输入和输出信号的权重。结果表明，在关联正系统的稳定性分析中，加权L1增益起着至关重要的作用。更确切地说，作为本文的主要结果，我们表明，一个互联的正系统是稳定的当且仅当存在一组加权向量，使每个积极的子系统的L1增益小于单位。因此，使用文献中的术语，加权向量作为“分离器”，因此我们建立了基于固体分离器的互连正系统的稳定性条件。我们最后说明，这些分离器为基础的条件是有效的，特别是当我们处理的鲁棒稳定性分析的正系统对L1增益有界和参数不确定性。
In this paper, we focus on L1 gain analysis problems of linear time-invariant continuous-time positive systems. A positive system is characterized by the strong property that its output is always nonnegative for any nonnegative input. Because of this peculiar property, it is natural to evaluate the magnitude of positive systems by the L1 gain (i.e. the L1 induced norm) in terms of the input and output signals. In contrast with the standard L1 gain, in this paper, we are interested in L1 gains with weightings on the input and output signals. It turns out that the L1 gain with weightings plays an essential role in the stability analysis of interconnected positive systems. More precisely, as a main result of this paper, we show that an interconnected positive system is stable if and only if there exists a set of weighting vectors that renders the L1 gain of each positive subsystem less than unity. As such, using a terminology in the literature, the weighting vectors work as 'separators,' and thus we establish solid separator-based conditions for the stability of interconnected positive systems. We finally illustrate that these separator-based conditions are effective particularly when we deal with robust stability analysis of positive systems against both L1 gain bounded and parametric uncertainties.