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Mathematics 2019, 7(1), 101; https://doi.org/10.3390/math7010101

Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay

1
School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China
2
Department of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
Received: 28 November 2018 / Revised: 29 December 2018 / Accepted: 15 January 2019 / Published: 18 January 2019
(This article belongs to the Section Mathematics and Computers Science)
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Abstract

This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued systems are provided by constructing a novel Lyapunov–Krasovskii functional, using an integral inequality technique, and reciprocal convex combination approach. The gained global μ -stability conditions can be divided into three different kinds of stability forms by varying the positive continuous function μ ( t ) . Finally, three reliable examples and a simulation are given to display the effectiveness of the proposed methods. View Full-Text
Keywords: quaternion-valued neutral-type neural network; homeomorphism theory; new reciprocal convex combination approach; linear matrix inequality; global μ-stability quaternion-valued neutral-type neural network; homeomorphism theory; new reciprocal convex combination approach; linear matrix inequality; global μ-stability
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Shu, J.; Xiong, L.; Wu, T.; Liu, Z. Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay. Mathematics 2019, 7, 101.

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