Absolute stability and dissipativity of continuous time multilayer recurrent neural networks

In this paper we present a sufficient condition for global asymptotic stability of continuous time multilayer recurrent neural networks with two-hidden layers. The condition is based on a Lur´e-Postnikov Lyapunov function and is expressed as a matrix inequality. With respect to input/output stability a condition for dissipativity is derived, which includes, for example, the cases of passivity and finite L₂-gain. This result is based on a quadratic storage function plus integral term. For nonlinear modelling and control purposes it enables to modify the classical dynamical backpropagation algorithm with a matrix inequality constraint in order to guarantee stable identified models or stable closed-loop control schemes, in a similar fashion has this can be done in discrete time NL _q theory