An extended generalized integral inequality based on free matrices and its application to stability analysis of neural networks with time-varying delays
SCIE
SCOPUS
- Title
- An extended generalized integral inequality based on free matrices and its application to stability analysis of neural networks with time-varying delays
- Authors
- Lee, Jun Hui; Na, Hyeon-Woo; Park, PooGyeon
- Date Issued
- 2023-02
- Publisher
- Pergamon Press Ltd.
- Abstract
- © 2022 The Franklin InstituteThis paper proposes an extended generalized integral inequality based on free matrices (EGIIFM) and applies it to the stability analysis of neural networks with time-varying delays. The EGIIFM estimates an upper bound for a quadratic form of a positive definite matrix with an augmented vector staked not only with the state and its derivative but also with the nonlinear activation function. By reflecting the correlated cross-information among the terms in the augmented vector as free matrices, the EGIIFM provides a tighter upper bound and encompasses various existing single integral inequalities as special cases. In addition, by establishing a new double integral Lyapunov–Krasovskii functional including the correlated cross-information, a less conservative stability criterion is obtained. Through three well-known numerical examples, the effectiveness of the EGIIFM is evaluated.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/117749
- DOI
- 10.1016/j.jfranklin.2022.12.042
- ISSN
- 0016-0032
- Article Type
- Article
- Citation
- Journal of the Franklin Institute, vol. 360, no. 3, page. 1690 - 1705, 2023-02
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