An online algorithm for the stability and regulation of discrete-time recurrent neural networks

A class of discrete-time recurrent neural networks is considered. An existing sufficient condition for the stability of such systems is given by Linear Matrix Inequalities (LMIs) in terms of positive definite diagonally dominant matrices. As neural networks are often tuned online, solving LMI problems from time to time to determine the stability can be a computational burden. This paper proposes an alternative approach, which uses an online algorithm to practically determine the stability of the systems. The main motive, however, is to extend this algorithm to the stabilization and regulation of such systems. Simulations show that the proposed algorithm is very effective in bringing the state of the neural networks back to zero.