The Lq/Lp Hankel Norms of Positive Systems

Yoshio Ebihara, Bohao Zhu, James Lam

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Article number8895893
Pages (from-to)462-467
Number of pages6
JournalIEEE Control Systems Letters
Issue number2
Publication statusPublished - Apr 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization


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