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>₂解析

<p>In this paper, we explore <i>H</i>₂analysis 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>₂norm 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>₂norm computation problem of a general LTI system to the <i>l</i><i>_∞</i>-induced norm computation problem (or <i>l</i>₁problem 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>₂norm of general discrete-time LTI systems.</p>