Input-Output Stability of Recurrent Neural Networks with Delays using Circle Criteria
Jochen J. Steil, Helge Joachim Ritter · 1998
We present a frequency domain analysis of additive recurrent neural networks based on the passivity approach to input-output stability. We apply graphical Circle Criteria for the case of normal weight matrices which result in effectively computable stability bounds, including systems with delay. Approximation techniques yield further generalisation to arbitrary matrices. Keywords: recurrent neural network, inputoutput stability, delay, circle criteria. 1 Introduction One strong motivation for research on recurrent neural network (RNN) models is their capability to model arbitrary temporal behaviour. Because there are a number of learning procedures available, which incrementally adapt a RNN to perform a desired transform from time-varying inputs to timevarying outputs [11], recurrent networks are found in a number of application areas and frequently used as components in larger systems [13, 9]. In this setting we regard a network as operator acting on inputs and then a basic requirem...