Global Stability of Phase-Change Neural Networks With Mixed Time Delays

Phase-change memory (PCM) is a novel type of nonvolatile memory and is suitable for artificial neural synapses. This article investigates the Lagrange global exponential stability (LGES) of a class of PCNNs with mixed time delays. First, based on the conductivity characteristics of PCM, a piecewise equation is established to describe the electrical conductivity of PCM. By using the proposed piecewise equation to simulate the neural synapses, a novel PCNN with discrete and distributed time delays is proposed. Then, using comparative theory and fundamental inequalities, the LGES conditions based on the
$M$
-matrix are proposed in the sense of Filippov, and the exponential attractive set (EAS) is obtained based on
$M$
-matrix and external input. Moreover, the Lyapunov global exponential stability (GES) conditions of PCNNs without external input are obtained by using the inequality technique and eigenvalue theory, which is a form of
$M$
-matrix. Finally, two simulation examples are given to verify the validity of the obtained results.