Abstract: Proportional delay is an unbounded time-varying delay, which is different from constant delay, bounded time-varying delay and distributed delay. The proportional delay systems often play important roles in some fields such as physics, biology systems and control theory, but at present there are not much dynamics behavior research of neural networks with proportional delays. In this paper, the global exponential stability of a class of recurrent neural networks with multi-proportional delays is studied. Firstly, a class of recurrent neural networks with multi-proportional delays is transformed into the recurrent neural networks with constant delays and variable coefficients by the nonlinear transformation. Secondly, based on the properties of $M$-matrix, the homeomorphism mapping theorem, and the delay differential inequality technique, a delay-independent sufficient condition which ensures the existence, uniqueness and global exponential stability of the equilibrium point of such neural networks is confirmed. This condition depends on the connection weight matrix of neural networks and the activation function of neurons. Finally, the numerical examples verify that the theoretical results are effective and less conservative than previously existing results.

Key words: recurrent neural networks, proportional delays, global exponential stability, $M$-matrix, delay differential inequality