Stability Of Equilibria Of Neural Networks

Sufficient conditions for local and global asymptotic stability of equilibria of some general classes of neural networks are presented. In the event that the interconnection matrix is block diagonally stable it is shown that the equilibrium is globally asymptotically stable if the cells are dissipative at the equilibrium. For a special class of networks the conditions of dissipativity are reduced to more readily-tested conditions of passivity. Equilibria are shown to be asymptotically stable essentially if the cells are locally passive.