Absolute Stability of Hopfield Neural Network

In this chapter, we first discuss the relationship between the stability of Hopfield neural network, Lyapunov stability, and the invariant principle in the sense of LaSalle. Next, we describe the connection and difference between the Hopfield neural network and the Lurie control systems with multiple nonlinear controllers. Then, we introduce the concept of absolute stability for neural networks, and present the sufficient and necessary conditions for two types of neural networks. Finally, we discuss various sufficient conditions for the absolute stability of Hopfield neural network. Partial materials are chosen Forti et al. [27, 28] and Kaskurewicz et al. [50] (Sects. 12.3 and 12.4), Liao et al. [87, 88, 90] (Sect. 12.5), and Liu [98] (Sect. 12.6).