Stabilization of Markovian Jump Boolean Control Networks via Sampled-Data Control.

Area of Science:

• Control Theory
• Network Science
• Systems Biology

Background:

• Markovian jump Boolean control networks (MJBCNs) are complex systems with applications in biology.
• Achieving stabilization in such networks with sampled-data feedback presents significant challenges.

Purpose of the Study:

• To develop criteria for finite-time and asymptotic stabilization of MJBCNs using sampled-data state feedback controls (SDSFCs).
• To construct the corresponding feedback matrices for SDSFCs.

Main Methods:

• Utilizing the semi-tensor product (STP) to introduce an augmented variable.
• Analyzing the Markov property of the augmented variable sequence under SDSFCs.
• Establishing convergence criteria for the switching signal and augmented variable.

Main Results:

• Derived sufficient and necessary criteria for both finite-time and asymptotic stabilization of MJBCNs.
• Successfully constructed feedback matrices for SDSFCs to achieve the desired stabilization.
• Demonstrated the applicability of the methods to biological networks.

Conclusions:

• The proposed SDSFC approach effectively achieves finite-time and asymptotic stabilization for MJBCNs.
• The developed criteria and control designs are robust and applicable to real-world biological models.
• This work advances the control of complex biological networks.