Local stability of recurrent networks with time-varying weights and inputs

Abstract

We present local conditions for stability of recurrent neural networks with time-varying parameters. Our constructive approach guarantees that a recurrent network implements a proper mapping from time-varying input to time-varying output functions using a local equilibrium as point of operation. The corresponding bounds on the allowed inputs and time-variation are defined by linear matrix inequalities and can be obtained numerically efficient by means of interior point optimisation schemes. We compare the method to the standard Lyapunov approach and apply it to an example of learning an input–output map implied by the chaotic Roessler attractor.