Contents I. Introduction
In recent years, many neural networks have been developed to solve various problems. In the design and hardware implementation of neural networks, however, a common problem is that parameters used or acquired in neural networks are inaccurate. To design neural networks, vital data such as the neuron firing rate and synaptic interconnection weights usually need to be measured, acquired, and processed by means of statistical estimation which inevitably leads to estimation errors. Moreover, parameter fluctuation in neural-network circuits is also unavoidable. In practice, we can actually obtain the range of the vital data and the bounds of circuit parameters through engineering experience or from incomplete information. This fact implies that a good neural network should be robust. Otherwise, the neural network is not very reliable in the practical applications. When we apply an interval neural network having certain robustness properties to solve optimization problems, we need not consider spurious suboptimal responses for each parameter value of the network, which is of great importance. Therefore, besides asymptotic and exponential stability of neural networks which has been studied by many researchers (see, e.g., [1] [2]–[15]), robust stability of neural networks has also received wide attention (see, e.g., [16]–[27]). Furthermore, most of the existing results on robust stability of neural networks are for continuous-time neural networks. There has been far less research studying the interesting problem of robust stability for discrete-time neural networks.
