State estimation for delayed genetic regulatory networks based on passivity theory

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.