Convergence in discrete-time neural networks with specific performance
Tianguang Chu · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2001
We analyze convergence in discrete-time neural networks with specific performance such as decay rate and trajectory bounds in terms of componentwise absolute (exponential) stability. Simple necessary and sufficient stability and positive invariance conditions are presented, which allow us to design a convergent network with prescribed performance. Our approach is based on a decomposition of competitive-cooperative connectivity or inhibitory-excitatory interaction that abounds in neural networks, without assuming symmetry of the connection matrices. The key idea is that through the decomposition, we can always relate a competitive-cooperative network with a cooperative dynamical system. The latter possesses significant order-preserving properties that are basic to our analysis. The explicit division of connection weights into inhibitory and excitatory types offers a higher potential for relating formal neural network models to neurophysiology.