Optimal and robust design of brain-state-in-a-box neural associative memories

This paper presents a new optimization approach to the design of associative memories via the brain-state-in-a-box (BSB) neural network. The optimization approach proposed in this paper provides the large and uniform domains of attraction of the prototype patterns, the large robustness margin for the weight matrix of the perturbed BSB neural network, the asymptotic stability of the prototype patterns, and the global stability of the BSB neural network. Based on some known qualitative properties of the BSB neural network and theoretical results presented in this paper, a synthesis method of the BSB-based associative memory is established. The synthesis method presented in this paper is given in the form of a linear matrix inequality-based optimization problem, which can be efficiently solved by a readily available software. Design examples are given to demonstrate the applicability of the proposed method and to compare with the existing synthesis methods.