Global asymptotic stability for a class of nonsymmetric neural networks

The authors show that the property of global asymptotic stability is guaranteed for a class of neural circuits with a special form of nonsymmetric interconnection matrix. They also show that neural networks used to solve typical optimization problems such as linear and quadratic programming problems fall into the class of circuits studied here and are characterized by a unique globally asymptotically stable equilibrium. The results are proved by means of the Lyapunov method and by finding suitable Lyapunov functions that are valid for special classes of neural networks with nonsymmetric interconnection matrices as described