TY - JOUR
T1 - The Lq/Lp Hankel Norms of Positive Systems
AU - Ebihara, Yoshio
AU - Zhu, Bohao
AU - Lam, James
N1 - Funding Information:
Manuscript received September 27, 2019; accepted November 5, 2019. Date of publication November 11, 2019; date of current version November 20, 2019. This work was supported in part by JSPS KAKENHI under Grant JP18K04200. Recommended by Senior Editor M. Arcak. (Corresponding author: Yoshio Ebihara.) Y. Ebihara is with the Department of Electrical Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan (e-mail: ebihara.yoshio.5r@kyoto-u.ac.jp).
Publisher Copyright:
© 2017 IEEE.
PY - 2020/4
Y1 - 2020/4
N2 - This letter is concerned with the Lq/Lp Hankel norms of linear time-invariant positive systems, where the Hankel norms are defined as the induced norms from vector-valued Lp -past inputs to vector valued Lq -future outputs. The Lq/Lp Hankel norms are studied in detail for general (nonpositive) LTI systems, and closed-form formulas have been derived for their characterization. However, some of them unavoidably include the absolute integral of impulse responses and/or implicit functions in their characterization and hence there remain difficulties in practical computation. In this letter we show that such difficulties are circumvented for positive systems, where positivity drastically facilitates the characterization of the past input that attains the Hankel norm. We also provide linear-programming- and semidefinite-programming-based characterizations of the Lq/Lp Hankel norms of positive systems, which are useful in the case where we analyze the Lq/Lp Hankel norms of positive systems affected by parametric uncertainties.
AB - This letter is concerned with the Lq/Lp Hankel norms of linear time-invariant positive systems, where the Hankel norms are defined as the induced norms from vector-valued Lp -past inputs to vector valued Lq -future outputs. The Lq/Lp Hankel norms are studied in detail for general (nonpositive) LTI systems, and closed-form formulas have been derived for their characterization. However, some of them unavoidably include the absolute integral of impulse responses and/or implicit functions in their characterization and hence there remain difficulties in practical computation. In this letter we show that such difficulties are circumvented for positive systems, where positivity drastically facilitates the characterization of the past input that attains the Hankel norm. We also provide linear-programming- and semidefinite-programming-based characterizations of the Lq/Lp Hankel norms of positive systems, which are useful in the case where we analyze the Lq/Lp Hankel norms of positive systems affected by parametric uncertainties.
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U2 - 10.1109/LCSYS.2019.2952622
DO - 10.1109/LCSYS.2019.2952622
M3 - Article
AN - SCOPUS:85075631396
VL - 4
SP - 462
EP - 467
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
SN - 2475-1456
IS - 2
M1 - 8895893
ER -