Motivated by recent advances in the study of linear time-invariant (LTI) positive systems, we explore analysis techniques of general, not necessarily positive, LTI systems using positive system theory. Even though a positive system is characterized by its peculiar property that its impulse response is nonnegative, we often deal with nonnegative impulse responses even in general LTI system analysis. A typical example is the computation of the H2 norm, where we focus on squared impulse responses. To deal with such products of impulse responses in a systematic fashion, in this paper, we first establish a construction technique of an LTI system whose impulse response is given by the product of impulse responses of two different LTI systems. Then, as the main result, we reduce the H2 norm computation problem of a general LTI system into the L∞-induced norm computation problem (or L1 problem in short) of a positive system, by which we can derive various formulas for the H2 norm computation.

中文翻译：

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$H_2$ 通过转换为外部正系统来分析 LTI 系统


受线性时不变 (LTI) 正系统研究最新进展的推动，我们使用正系统理论探索一般（不一定是正）LTI 系统的分析技术。尽管正系统的特点是其脉冲响应是非负的，但即使在一般的 LTI 系统分析中，我们也经常处理非负脉冲响应。一个典型的例子是 H2 范数的计算，其中我们关注平方脉冲响应。为了以系统的方式处理此类脉冲响应乘积，在本文中，我们首先建立了一种 LTI 系统的构造技术，其脉冲响应由两个不同 LTI 系统的脉冲响应的乘积给出。然后，作为主要结果，我们将一般LTI系统的H2范数计算问题简化为正系统的L∞诱导范数计算问题（或简称L1问题），由此我们可以推导出H2的各种公式范数计算。