Journal
MATHEMATICS
Volume 8, Issue 5, Pages -Publisher
MDPI
DOI: 10.3390/math8050815
Keywords
stochastic memristive quaternion-valued neural networks; exponential input-to-state stability; Lyapunov fractional
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Funding
- King Mongkut's University of Technology Thonburi (KMUTT)
- Thailand research Grant Fund [RSA6280004]
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In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying Ito's formula, Dynkin's formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.
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