  We consider the method of Reduction of Dissipativity Domain to prove global
Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and
advanced criteria for Absolute Stability of these essentially nonlinear systems
produce rather weak results. The method mentioned above is proved to be more
powerful. It involves a multi-step procedure with maximization of special
nonconvex functions over polytopes on every step. We derive conditions which
guarantee an existence of at most one point of local maximum for such functions
over every hyperplane. This nontrivial result is valid for wide range of neuron
transfer functions.
