外部非負システムへの変換による離散時間線形時不変システムの<i>H</i><sub>2 </sub>解析

Translated title of the contribution: <i>H</i><sub>2 </sub>Analysis of LTI Discrete-Time Systems via Conversion to Externally Positive Systems

蛯原 義雄, 瀬部 昇, 増淵 泉, 脇 隼人, 管野 政明, 椿野 大輔

Research output: Contribution to journalArticlepeer-review

Abstract

<p>In this paper, we explore <i>H</i><sub>2 </sub>analysis techniques of general, not necessarily positive, discrete-time linear time-invariant (LTI) systems by means of positive system theory. While externally positive systems are a particular class of systems whose impulse responses take only nonnegative values, we often encounter such impulse responses even in the analysis of general LTI systems. A typical example is the computation of the <i>H</i><sub>2 </sub>norm where we focus on squared impulse responses. In view of this observation, we first clarify that we can construct an SISO externally positive system whose impulse response is given by the square of the impulse response of a given SISO LTI system. This system conversion allows us to reduce the <i>H</i><sub>2 </sub>norm computation problem of a general LTI system to the <i>l</i><i><sub>∞</sub></i>-induced norm computation problem (or <i>l</i><sub>1 </sub>problem in short) of the resulting externally positive system. It also turns out that this problem reduction enables us to derive various alternative formulas for the <i>H</i><sub>2 </sub>norm of general discrete-time LTI systems.</p>
Translated title of the contribution<i>H</i><sub>2 </sub>Analysis of LTI Discrete-Time Systems via Conversion to Externally Positive Systems
Original languageJapanese
Pages (from-to)75-84
Number of pages10
Journalシステム制御情報学会論文誌
Volume31
Issue number2
DOIs
Publication statusPublished - 2018

Fingerprint Dive into the research topics of '<i>H</i><sub>2 </sub>Analysis of LTI Discrete-Time Systems via Conversion to Externally Positive Systems'. Together they form a unique fingerprint.

Cite this