Projection Neural Network System Stability Study

Projection neural network play an important role in solving optimization problems. Optimization problems have wide applications in scientific and engineering. Many engineering problems, such as optimal control, structure design, mechanical design, and electrical networks planning, can be formulated as constrained nonlinear optimization problems. Thus the studies of the stabilities of projection neural networks have important theoretical significance and practical application values.In this thesis, we focus on the studies of the stabilities of no time-delayed projection neural networks and neutral-type delayed projection neural networks. We use the theorem of Lyapunov and the method of variation-of-constants to study the stabilities of neural networks. There are two main conclusions:1. ON the studies of the stabilities of no time-delayed projection neural networks, we use the theorem of Lyapunov,and get the stability conditions of the system.2. ON the studies of the stabilities of neutral-type delayed projection neural networks, we use the variation-of-constants, and get the stability conditions of the system.