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Related Experiment Video

Updated: May 11, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

State estimation for delayed genetic regulatory networks based on passivity theory.

V Vembarasan1, G Nagamani, P Balasubramaniam

  • 1Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram 624 302, Tamilnadu, India. vembarasanv@gmail.com

Mathematical Biosciences
|May 28, 2013
PubMed
Summary

This study develops a state estimation method for genetic regulatory networks with time-varying delays using passivity analysis. The approach effectively approximates gene and protein concentrations, enhancing control system design.

Keywords:
Genetic regulatory networksLyapunov–Krasovskii functionalsPassivity theoryState estimation

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Area of Science:

  • Systems Biology
  • Control Theory
  • Network Science

Background:

  • Genetic regulatory networks (GRNs) are crucial for cellular functions.
  • Accurate state estimation in GRNs is essential for understanding and controlling biological processes.
  • Time delays are inherent in GRN dynamics and complicate state estimation.

Purpose of the Study:

  • To design a state estimator for delayed genetic regulatory networks (GRNs).
  • To approximate the true concentrations of mRNA and protein using available measurement outputs.
  • To address non-differentiable and unconstrained time-varying delays in GRNs.

Main Methods:

  • Utilizing a passivity analysis approach for state estimation.
  • Developing Lyapunov-Krasovskii functionals with triple integral terms.
  • Applying integral inequalities and convex combination techniques.
  • Establishing a delay-dependent passivity criterion formulated as linear matrix inequalities (LMIs).

Main Results:

  • A novel passivity criterion for GRNs with time-varying delays is established.
  • The proposed method removes constraints on the derivative of time-varying delays.
  • The criterion is expressed in LMIs, ensuring efficient solvability.
  • Numerical examples demonstrate the effectiveness of the estimation schemes.

Conclusions:

  • The proposed state estimation method is effective for delayed GRNs.
  • The approach handles complex time-varying delays.
  • The LMI-based formulation facilitates practical implementation and control system design.