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

This study investigates the extended dissipativity analysis for uncertain delayed genetic regulatory networks (GRNs) within an interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. To the best of our knowledge, this is the first attempt to capture the complex dynamics and parameter uncertainties of GRNs via IT2 fuzzy sets, providing a robust representation through lower and upper membership functions. By constructing a novel Lyapunov-Krasovskii (L-K) functional, explicit derivations of the maximum admissible delay bounds are obtained. A unified analytical framework is established to verify L₂ - L∞ performance, H∞ attenuation, passivity, and dissipativity. To further reduce conservatism, a membership-function-dependent (MFD) stability criterion is developed that fully exploits the characteristics of IT2 fuzzy sets. Numerical examples demonstrate that the proposed approach significantly outperforms existing methods in terms of less conservative stability conditions and improved dissipativity indices under uncertainties and delays. This work advances theoretical understanding and practical design of robust control strategies for GRNs, with potential applications in synthetic biology.