Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays

Area of Science:

• Control Theory
• Systems Biology
• Computational Intelligence

Background:

• Genetic regulatory networks (GRNs) are crucial for cellular functions.
• Takagi-Sugeno (T-S) fuzzy models are effective for representing complex biological systems.
• Sampled-data control is essential for systems with discrete-time measurements and continuous-time dynamics, particularly with leakage delays.

Purpose of the Study:

• To investigate the sampled-data stabilization problem for T-S fuzzy GRNs with leakage delays.
• To develop novel stability conditions using advanced Lyapunov-Krasovskii functionals (LKFs).
• To propose a new method for designing sampled-data controllers based on linear matrix inequalities (LMIs).

Main Methods:

• Construction of a novel Lyapunov-Krasovskii functional (LKF) by non-uniformly dividing delay intervals with triplex and quadruplex integral terms.
• Derivation of new stability conditions for both constant and time-varying delay cases within the T-S fuzzy framework.
• Formulation of a sampled-data controller design condition using linear matrix inequality (LMI) representation.

Main Results:

• New stability criteria for T-S fuzzy GRNs with leakage delays are established using the proposed LKFs.
• A novel sampled-data controller design method is presented, ensuring system stability.
• A numerical example demonstrates the efficacy and applicability of the developed control design method.

Conclusions:

• The proposed LKF-based approach effectively addresses the sampled-data stabilization of T-S fuzzy GRNs with leakage delays.
• The developed LMIs provide a systematic way to design stabilizing controllers for such complex biological systems.
• The findings contribute to robust control strategies for biologically inspired computational systems.