TY - GEN

T1 - Hz analysis of LTI systems via conversion to positive systems

AU - Ebihara, Yoshio

PY - 2017/11/10

Y1 - 2017/11/10

N2 - Motivated by recent drastic advances in the study of linear-time invariant (ETI) positive systems, we explore analysis techniques of general, not necessarily positive ETI 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 ETI 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 ETI system whose impulse response is given by the product of impulse responses of two different ETI systems. Then, as the main result, we reduce the H2 norm computation problem of a general ETI system into the L∞-induced norm computation problem (or L1 problem in short) of a positive system, by which we can derive a closed-form formula for the H∞ norm computation.

AB - Motivated by recent drastic advances in the study of linear-time invariant (ETI) positive systems, we explore analysis techniques of general, not necessarily positive ETI 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 ETI 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 ETI system whose impulse response is given by the product of impulse responses of two different ETI systems. Then, as the main result, we reduce the H2 norm computation problem of a general ETI system into the L∞-induced norm computation problem (or L1 problem in short) of a positive system, by which we can derive a closed-form formula for the H∞ norm computation.

UR - http://www.scopus.com/inward/record.url?scp=85044109877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044109877&partnerID=8YFLogxK

U2 - 10.23919/SICE.2017.8105544

DO - 10.23919/SICE.2017.8105544

M3 - Conference contribution

AN - SCOPUS:85044109877

T3 - 2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017

SP - 1216

EP - 1219

BT - 2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017

Y2 - 19 September 2017 through 22 September 2017

ER -