Decentralized control of interconnected positive systems using L 1-induced norm characterization

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier

Research output: Contribution to journalConference articlepeer-review

19 Citations (Scopus)


This study concerns decentralized control of interconnected positive systems. The main issue is how to design a controller for each subsystem locally so that positivity and stability of the overall interconnected system can be attained. Under a specific interconnection structure, we will show that such a controller can be designed optimally without any information about the rest of the positive subsystems. This achievement is based on our recent characterization of stability of interconnected positive systems in terms of the L1-induced norm of each subsystem, where the L1-induced norm is evaluated with positive weighting vectors that are coupled mutually over the subsystems. The key observation in this study is that, under the specific interconnection structure, we can decouple the L1-induced norm conditions completely. We thus reduce the original stabilization problem into a set of L1-induced norm optimal controller synthesis problems each of which can be solved indeed locally. In particular, the L1-induced norm optimal controller synthesis can be done efficiently by solving a semidefinite programming problem.

Original languageEnglish
Article number6427022
Pages (from-to)6653-6658
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Publication statusPublished - 2012
Externally publishedYes
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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