Stability Analysis of Block Logical Dynamical Systems and Its Application in Logical Networks With Time Delay

• Published in: IEEE transactions on automatic control Vol. 69; no. 10; pp. 7211 - 7215
• Main Authors: Li, Haitao, Li, Yalu, Li, Wenrong, Liu, Yansheng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algebraic state space representation; block logical dynamical system (BLDS); Circuit stability; Delay effects; Dynamical systems; logical network; Networks; Nonlinear systems; Regulation; stability; Stability analysis; Stability criteria; time delay; Time lag; Vectors
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3394549

A new class of nonlinear systems, block logical dynamical systems (BLDSs), is introduced in this note. The existence and uniqueness of solution to BLDSs are first investigated. Then, the topological structure and global stability of BLDSs are analyzed, and a novel criterion is presented to verify the global stability of BLDSs. Finally, the stability of BLDSs is used to study the stability of logical networks subject to time delay. It is shown that the introduction of BLDSs can considerably reduce the computational complexity of verifying the stability of logical networks with time delay.