Robust Set Stability for Switched Boolean Networks Under One-Bit Function Perturbation

Abstract

This paper investigates robust set stability for the switched Boolean networks (SBNs) with arbitrary switching signal affected by one-bit function perturbation (OBFP). Firstly, the dynamics of these networks are converted into algebraic forms utilizing semi-tensor product (STP) method. Secondly, OBFP impact on the set stability of SBNs is divided into four cases. Then, by constructing a state set and defining an index vector, several necessary and sufficient conditions are provided to detect whether an SBN with arbitrary switching signal is still stable to the given set after OBFP. Finally, a biological example is proposed to demonstrate the effectiveness of the obtained theoretical results.

Keywords

• Switched Boolean networks
• semi-tensor product of matrices
• set stability
• one-bit function perturbation
• arbitrary switching signal