Reduced- and Full-Order Observers for Delayed Genetic Regulatory Networks

Area of Science:

• Systems Biology
• Control Theory
• Biochemical Engineering

Background:

• Genetic regulatory networks (GRNs) are complex biological systems with inherent time delays.
• Accurate state estimation of mRNA and protein concentrations is crucial for understanding GRN dynamics.
• Existing methods may not adequately address the challenges posed by time delays in GRNs.

Purpose of the Study:

• To design reduced-order and full-order state observers for delayed genetic regulatory networks.
• To estimate the concentrations of mRNAs and proteins within these networks.
• To ensure the asymptotic stability of the error system.

Main Methods:

• A Lyapunov-Krasovskii functional incorporating quadruplicate integrals was introduced.
• Wirtinger-type integral inequalities, reciprocal convex, and convex techniques were employed to estimate the functional's derivative.
• Delay-dependent sufficient conditions were derived in the form of linear matrix inequalities (LMIs).

Main Results:

• Sufficient conditions for asymptotic stability of the error system were established using LMIs.
• Observer gains for both reduced-order and full-order observers were determined via LMI solutions.
• Concrete expressions for the state observers were presented.

Conclusions:

• The proposed method effectively estimates states in delayed genetic regulatory networks.
• The derived LMIs provide a robust framework for ensuring system stability.
• Simulation results confirm the validity and efficacy of the developed state observers.