A new neural network model and its application

Abstract

A novel neural network model called standard neural network model (SNNM) was advanced, which was the interconnection of a linear dynamic system and a bounded static nonlinear operator. The SNNM could be represented by linear differential inclusion (LDI), which allowed us to take advantage of the linear matrix inequality (LMI) approach in the stability analysis or other performance analysis of the SNNM. By combining a number of different Lyapunov functions with S-procedure, some useful stability theorems for continuous time SNNM (CSNNM) and discrete time SNNM (DSNNM) were derived, whose conditions were formulated as LMIs. Some examples for the application of the SNNMs were presented, such as analyzing the stability of recurrent neural network (RNN), analyzing or synthesizing the neural network control system etc.