Optimal L1-controller synthesis for positive systems and its robustness properties

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier

Research output: Chapter in Book/Report/Conference proceedingConference contribution

50 Citations (Scopus)


In a recent study, we introduced an L1-induced norm (L 1 gain in short) as a performance index for linear time-invariant positive systems, where the L1-norm of the disturbance input and the performance output signals is evaluated with positive weighting vectors. Moreover, we showed that the L1 gain with the weighting vectors plays an essential role in stability analysis of interconnected positive systems. Aiming at extending this result for stabilization of interconnected positive systems, in this paper, we study L1-optimal feedback controller synthesis for positive systems with given weighing vectors. In particular, we will show that an L1-optimal state-feedback gain designed for a fixed positive system and a fixed pair of weighing vectors is robustly optimal against variations on the input matrix, the direct feedthrough matrix of the controlled positive system as well as variations on the weighting vector for the disturbance input signal. This property is of course promising for robust L1-optimal control of uncertain positive systems. We illustrate the robust optimality property by numerical examples.

Original languageEnglish
Title of host publication2012 American Control Conference, ACC 2012
Number of pages6
Publication statusPublished - 2012
Externally publishedYes
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2012 American Control Conference, ACC 2012
CityMontreal, QC

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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