H2 Analysis of LTI Systems via Conversion to Externally Positive Systems

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...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 63; H. 8; S. 2566 - 2572
1. Verfasser: Ebihara, Yoshio
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 01.08.2018
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<named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> H_2</tex-math> </inline-formula> </named-content> norm
<named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> L_\infty</tex-math> </inline-formula> </named-content>-induced norm
Ear
Economics
Indexes
Linear systems
MIMO
positive system
system conversion
Systematics
Systems operation
ISSN:0018-9286
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Zusammenfassung: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 <inline-formula><tex-math notation="LaTeX">H_2</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">H_2 </tex-math></inline-formula> norm computation problem of a general LTI system into the <inline-formula> <tex-math notation="LaTeX">L_\infty</tex-math></inline-formula>-induced norm computation problem (or <inline-formula> <tex-math notation="LaTeX">L_1</tex-math></inline-formula> problem in short) of a positive system, by which we can derive various formulas for the <inline-formula><tex-math notation="LaTeX">H_2</tex-math></inline-formula> norm computation.
ISSN:0018-9286
DOI:10.1109/TAC.2017.2767704