Global μ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays.

In this paper, we first propose quaternion-valued neural networks (QVNNs) with unbounded time-varying delays. Some sufficient conditions on the global µ-stability in the form of both complex-valued and real-valued linear matrix inequalities (LMIs) are provided by solving two difficulties. One is decomposing the QVNN into two complex-valued systems with the plural decomposition method of quaternion, which can reduce the complexity of calculations by avoiding the non-commutativity of quaternion multiplication. The other is choosing the appropriate Lyapunov-Krasovskii functional in the form of Hermitian matrices, which is a big challenge. Finally, two numerical examples are provided to verify the effectiveness of the obtained results.