Structurally quotient fixed modes

Guilherme Ramos, A. Pedro Aguiar, Sérgio Pequito

Research output: Contribution to journalArticleScientificpeer-review


We provide a necessary and sufficient graph-theoretical characterization of quotient fixes modes occurring in parametric decentralized control systems. Specifically, we introduce the notion of structurally quotient fixed modes (SQFMs) that generically captures the quotient fixed modes and only depends on the system's structure. Additionally, we provide an efficient polynomial-time algorithm for the verification of this graph-theoretical condition. We show that this algorithm can be parallelized, and linear-time computational complexity approximation algorithms can be considered to attain a sub-optimal solution. Lastly, we discuss the implications of the actuation–sensing–communication capabilities and the systems’ interconnections on the existence of SQFM.

Original languageEnglish
Article number104914
Number of pages7
JournalSystems and Control Letters
Publication statusPublished - 2021


  • Decentralized control
  • Large-scale systems
  • Quotient fixed modes
  • Structural systems


Dive into the research topics of 'Structurally quotient fixed modes'. Together they form a unique fingerprint.

Cite this