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Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method.

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Title: Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method.
Authors: Wang, Chen-Rui1,2 (AUTHOR) wangcr@cug.edu.cn, He, Yong1,2 (AUTHOR) heyong08@cug.edu.cn, Lin, Wen-Juan1,2 (AUTHOR) linwenjuan@cug.edu.cn
Source: Applied Mathematics & Computation. Feb2021, Vol. 391, pN.PAG-N.PAG. 1p.
Subjects: Stability criterion, Conservatism, Problem solving
Abstract: • An improved Lyapunov-Krasovskii functional (LKF) is proposed by considering more key information about delay states, integral terms and the activation function and can get a less conservative stability criterion. • A new relaxed quadratic function negative-determination provides a valid way to deal with the problem of the negative quadratic function. The generalized reciprocally convex combination is been used to solve the problem of the delay function τ ˙ (t) in the denominator. Combining the novel augmented LKF itself and its derivative with both of the above methods, a new less conservative stability criterion is obtained. • In addition, the difference with the previous researches is that the MADBs are obtained by the stability condition with the value of the delay τ (t) bound information rather than using the value of its derivative. It is worth noting that the criterion removes the derivative constraint of time-varying delay, which means fast-varying delay is allowed. • Some numerical examples are presented to prove the effectiveness and lower conservatism of the new stability criterion. This paper studies the problem of stability analysis of generalized neural networks (GNN) with a fast-varying delay. Firstly, an improved augmented Lyapunov-Krasovskii functional (LKF) is proposed by fully considering more states information about interrelated systems and neuron activation function conditions. Then, to handle the derivative of the LKF, the generalized reciprocally convex combination and a relaxed quadratic function negative-determination are employed. Based on these methods and the augmented LKF, a less conservative delay-dependent stability criterion for GNN with a fast-varying delay is presented. Finally, some numerical examples are given to demonstrate the effective superiority of the proposed criterion. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:• An improved Lyapunov-Krasovskii functional (LKF) is proposed by considering more key information about delay states, integral terms and the activation function and can get a less conservative stability criterion. • A new relaxed quadratic function negative-determination provides a valid way to deal with the problem of the negative quadratic function. The generalized reciprocally convex combination is been used to solve the problem of the delay function τ ˙ (t) in the denominator. Combining the novel augmented LKF itself and its derivative with both of the above methods, a new less conservative stability criterion is obtained. • In addition, the difference with the previous researches is that the MADBs are obtained by the stability condition with the value of the delay τ (t) bound information rather than using the value of its derivative. It is worth noting that the criterion removes the derivative constraint of time-varying delay, which means fast-varying delay is allowed. • Some numerical examples are presented to prove the effectiveness and lower conservatism of the new stability criterion. This paper studies the problem of stability analysis of generalized neural networks (GNN) with a fast-varying delay. Firstly, an improved augmented Lyapunov-Krasovskii functional (LKF) is proposed by fully considering more states information about interrelated systems and neuron activation function conditions. Then, to handle the derivative of the LKF, the generalized reciprocally convex combination and a relaxed quadratic function negative-determination are employed. Based on these methods and the augmented LKF, a less conservative delay-dependent stability criterion for GNN with a fast-varying delay is presented. Finally, some numerical examples are given to demonstrate the effective superiority of the proposed criterion. [ABSTRACT FROM AUTHOR]
ISSN:00963003
DOI:10.1016/j.amc.2020.125631