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

Abstract

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.