Input–output gain analysis of positive periodic systems

Bohao Zhu, James Lam, Yoshio Ebihara

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


This paper investigates the input-output gains, including ℓ1- and ℓ-gains and L1- and L-gains, of discrete-time and continuous-time positive periodic systems. For the discrete-time case, the input–output gain can be characterized by linear inequalities. For the continuous-time case, the input–output gain characterization problem turns into the existence problem of a positive periodic vector function. Based on some necessary and sufficient input–output gain conditions, we find the ℓ1- (L1-) gain of discrete-time (continuous-time) positive periodic systems is equivalent to the of ℓ- (L-) gain of the associated dual systems. Finally, two numerical examples are given to illustrate the results.

Original languageEnglish
Pages (from-to)2928-2945
Number of pages18
JournalInternational Journal of Robust and Nonlinear Control
Issue number8
Publication statusPublished - May 25 2021

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • General Chemical Engineering
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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