An extended generalized integral inequality based on free matrices and its application to stability analysis of neural networks with time-varying delays. Issue 3 (February 2023)

• Record Type: Journal Article
• Authors: Lee, Jun Hui; Na, Hyeon-Woo; Park, PooGyeon
• Is Part Of: Journal of the Franklin Institute. Volume 360:Issue 3(2023)
• Page Start: 1690
• Page End: 1705
• Publication Date: 2023-02
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2022.12.042
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: This 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.