TY - JOUR

T1 - H2 Analysis of LTI systems via conversion to externally positive systems

AU - Ebihara, Yoshio

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2018/8

Y1 - 2018/8

N2 - 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 H-2 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 H-2 norm computation problem of a general LTI system into the L-\infty-induced norm computation problem (or L-1 problem in short) of a positive system, by which we can derive various formulas for the H-2 norm computation.

AB - 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 H-2 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 H-2 norm computation problem of a general LTI system into the L-\infty-induced norm computation problem (or L-1 problem in short) of a positive system, by which we can derive various formulas for the H-2 norm computation.

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U2 - 10.1109/TAC.2017.2767704

DO - 10.1109/TAC.2017.2767704

M3 - Article

AN - SCOPUS:85032733266

VL - 63

SP - 2566

EP - 2572

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 8

ER -