Robust stability analysis of geneprotein regulatory networks with cyclic activationrepression interconnections

Tae Hyoung Kim, Yutaka Hori, Shinji Hara

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


This paper investigates analytic robust stability criteria for large-scale cyclic geneprotein regulatory network systems consisting of genes with heterogeneous dynamics combined with parametric or unstructured uncertainties from a control-theoretic viewpoint. We first consider a class of gene expressions, which is described as an uncertain linear transcriptiontranslation model (LTTM) with feedback loops from translation products to transcription. Next, we show that such a model belong to a class of large-scale dynamical linear network systems with a generalized frequency variable. Then, we derive robust stability criteria systematically for the following two types of biological uncertain LTTM: (i) LTTMs consisting of heterogeneous gene dynamics with parametric uncertainties and (ii) LTTMs consisting of homogeneous nominal gene dynamics with unstructured uncertainties. These criteria provide fairly simple analysis methodologies, which can be readily applied to the analysis for large-scale genetic regulatory networks and give some biological insight.

Original languageEnglish
Pages (from-to)373-382
Number of pages10
JournalSystems and Control Letters
Issue number6
Publication statusPublished - 2011 Jun
Externally publishedYes


  • Geneprotein regulatory networks
  • Generalized frequency variable
  • Matrices with cyclic structure
  • Robust stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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