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Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition

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  • Pahnehkolaei, Seyed Mehdi Abedi
  • Alfi, Alireza
  • Machado, J.A. Tenreiro

Abstract

This paper studies the stability of fractional order (FO) continuous-time quaternion-valued Leaky Integrator Echo State Neural Networks (NN). The delay independent robust stability of NN with QUAD vector field activation functions under time varying delays is derived. The analysis follows the FO Lyapunov theorem while decomposing the NN into four real-valued systems. The existence and uniqueness of the equilibrium point are also verified by means of a contraction map on the decomposed NN. The new approach is tested in the stability analysis of the FO quaternion-valued Echo State NN whitout time delays, complex-valued Echo State and quaternion-/complex-valued Hopfield NN with/without time delays. Two numerical examples demonstrate the feasibility of the proposed method.

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  • Pahnehkolaei, Seyed Mehdi Abedi & Alfi, Alireza & Machado, J.A. Tenreiro, 2019. "Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 278-293.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:278-293
    DOI: 10.1016/j.amc.2019.04.083
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