Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 51, Issue 4, Pages 2142-2152Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2019.2946076
Keywords
Delays; Artificial neural networks; Synchronization; Control theory; Stability; Delay effects; Linear matrix inequalities; Complex-valued neural networks (CVNNs); inhibitory factors; matrix measure; proportional delays; stability; synchronization
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Funding
- National Natural Science Foundation of China [61673308]
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This article proposes a complex-valued neural network model with proportional delays and inhibitory factors, and derives criteria for ensuring its global exponential stability using the Halanay inequality technique and matrix measure method. By designing a feedback controller and providing limitation conditions, global exponential synchronization of two neural network models is achieved successfully.
In this article, complex-valued neural networks (CVNNs) with proportional delays and inhibitory factors are proposed. First, the global exponential stability of the model addressed is investigated by employing the Halanay inequality technique and the matrix measure method. Some criteria are derived to guarantee the global exponential stability of CVNNs with proportional delays and inhibitory factors. The obtained criteria are applicable not only to systems with proportional delays but also to systems with arbitrary delays. Here, the Lyapunov functions are not constructed. Compared with the Lyapunov method, the matrix measure method makes the obtained criteria more concise, and the Halanay inequality makes the analytical procedure more compact. Furthermore, the global exponential synchronization of two neural-network models with proportional delays and inhibitory factors is also studied. By designing a feedback controller and giving some limitation conditions, the drive system and the response system realize global exponential synchronization. Finally, numerical simulation examples are provided to validate the effectiveness of the theoretical results obtained.
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