Global Exponential Stability of a Class of Memristor-Based RNN and Its Application to Design Stable Voltage Circuits

Abstract

In this article, we study the global exponential stability of the equilibrium point for a class of memristor-based recurrent neural networks (MRNNs). The MRNNs are based on a realistic memristor model and can be implemented by a very large scale of integration circuits. By introducing a proper Lyapunov functional, it is proved that the equilibrium point of the MRNN is globally exponentially stable under two less conservative assumptions. Furthermore, an algorithm is proposed for the design of MRNN-based circuits with stable voltages. Finally, an illustration example is performed to show the validation of the proposed theoretical results; an MRNN-based circuit with stable voltages is designed according to the proposed algorithm.