A synthesis method for the complex-valued associative memory constrained by the attractive domain

A synthesis method for the complex-valued Hopfield network functioned as an associate memory is introduced. Our aim is to guarantee the stored complex-valued patterns are asymptotically stable equilibrium points of the network in the given attractive domain. To this aim we firstly utilize equilibrium equations and Pseudoinverse calculation to obtain the relationship between time constant and connection weights of the network. Then in a given local domain around one equilibrium point we analyze the stability of the complex-valued network and derive the stability condition by Lyapunov theory. The stability conditions are expressed as linear matrix inequalities (LMIs) in the terms of all the varying parameters and hence the network can be easily designed.