Type-Dependent Average Dwell Time Method and Its Application to Delayed Neural Networks With Large Delays

• Published in: IEEE transaction on neural networks and learning systems Vol. 35; no. 2; pp. 2875 - 2880
• Main Authors: Wang, Hui-Ting, He, Yong, Zhang, Chuan-Ke
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Allowable maximum delay bound (AMDB); average dwell time (ADT); Biological neural networks; delayed neural network; Delays; Dwell time; large delay; Liapunov functions; multiple Lyapunov functions (MLFs); Neural networks; Numerical stability; Stability criteria; State vectors; Subsystems; switch; Switches; Symmetric matrices; Thermal stability
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2022.3184712

This article investigates the stability of delayed neural networks with large delays. Unlike previous studies, the original large delay is separated into several parts. Then, the delayed neural network is viewed as the switched system with one stable and multiple unstable subsystems. To effectively guarantee the stability of the considered system, the type-dependent average dwell time (ADT) is proposed to handle switches between any two sequences. Besides, multiple Lyapunov functions (MLFs) are employed to establish stability conditions. Adding more delayed state vectors increases the allowable maximum delay bound (AMDB), reducing the conservatism of stability criteria. A general form of the global exponential stability condition is put forward. Finally, a numerical example illustrates the effectiveness, and superiority of our method over the existing one.