Robust stability of Boolean networks with data loss and disturbance inputs
Xiao Wang1, Jianwei Xia1, Jun-E Feng2
1Research Center of Semi-tensor Product of Matrices: Theory and Applications, School of Mathematical Sciences, Liaocheng University, Liaocheng, 252000, Shandong, PR China.
Summary
This study addresses robust stability in Boolean networks (BNs) with data loss. A new method using semi-tensor product (STP) converts BNs into probabilistic systems for stability analysis.
Area of Science:
- Control Theory
- Network Science
- Computer Science
Background:
- Boolean networks (BNs) are crucial for modeling complex systems.
- Ensuring robust stability in BNs with data loss and disturbances is a significant challenge.
- Existing methods may not adequately address probabilistic data loss scenarios.
Purpose of the Study:
- To develop a novel framework for analyzing the robust stability of Boolean networks with data loss and disturbances.
- To convert the original system into a probabilistic augmented system for simplified analysis.
- To establish criteria and algorithms for verifying robust stability.
Main Methods:
- Utilizing the semi-tensor product (STP) technique to transform Boolean networks into an algebraic form.
- Constructing a probabilistic augmented system to represent the original system with data loss.
- Developing criteria and an algorithm based on truth matrices for set stability verification.
Main Results:
- The robust stability problem of BNs with data loss is reformulated as a set stability problem for the augmented system.
- New criteria for robust stability are proposed.
- An algorithm for verifying robust set stability is developed and validated.
Conclusions:
- The proposed method effectively addresses the robust stability problem of Boolean networks with probabilistic data loss and disturbances.
- The conversion to a probabilistic augmented system simplifies stability analysis.
- The developed algorithm provides a reliable tool for assessing system stability.
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