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Trans-vivo Delayed Type Hypersensitivity Assay for Antigen Specific Regulation

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Extended Dissipative Analysis for Uncertain Delayed Genetic Regulatory Networks via Interval Type-2 T-S Fuzzy

Menglu Zhu, Yi Zeng, Yankui Shi

IEEE Transactions on Cybernetics

|January 19, 2026

Summary

This study introduces a novel interval type-2 fuzzy approach for analyzing uncertain genetic regulatory networks (GRNs) with delays. The method enhances stability and control design for these complex biological systems.

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Area of Science:

Systems Biology
Control Theory
Computational Biology

Background:

Genetic Regulatory Networks (GRNs) exhibit complex dynamics and parameter uncertainties.
Delayed systems and uncertainties pose significant challenges in GRN modeling and control.
Interval Type-2 (IT2) fuzzy logic offers enhanced capabilities for handling uncertainty compared to traditional fuzzy sets.

Purpose of the Study:

To develop an extended dissipativity analysis for uncertain delayed GRNs using an IT2 Takagi-Sugeno (T-S) fuzzy framework.
To establish a robust representation of GRN dynamics and parameter uncertainties via IT2 fuzzy sets.
To derive explicit bounds for maximum admissible delays and verify performance metrics.

Main Methods:

Construction of a novel Lyapunov-Krasovskii (L-K) functional.
Development of a unified analytical framework for ${\mathcal {L}}_{2}$ - ${\mathcal {L}}_{\infty }$ performance, $H_{\infty }$ attenuation, passivity, and dissipativity verification.
Implementation of a membership-function-dependent (MFD) stability criterion leveraging IT2 fuzzy set characteristics.

Main Results:

Explicit derivations of maximum admissible delay bounds were obtained.
The proposed IT2 fuzzy framework provides a robust representation of GRN dynamics.
Numerical examples show less conservative stability conditions and improved dissipativity indices compared to existing methods.

Conclusions:

The study presents a first-of-its-kind IT2 fuzzy approach for GRN analysis, effectively handling uncertainties and delays.
The developed methods advance theoretical understanding and practical design of robust control strategies for GRNs.
This work has potential applications in synthetic biology for designing more reliable biological circuits.