A Degree-Dependent Polynomial-Based Reciprocally Convex Matrix Inequality and Its Application to Stability Analysis of Delayed Neural Networks

• Published in: IEEE transactions on cybernetics Vol. 54; no. 7; pp. 4164 - 4176
• Main Authors: Wang, Chen-Rui, Long, Fei, Xie, Ke-You, Wang, Hui-Ting, Zhang, Chuan-Ke, He, Yong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.07.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Delays; High-order polynomials; Linear matrix inequalities; Neural networks; Polynomials; reciprocally convex matrix inequality (RCMI); stability; Stability analysis; Stability criteria; Symmetric matrices; Thermal stability; time-varying delay
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2024.3365709

In this article, several improved stability criteria for time-varying delayed neural networks (DNNs) are proposed. A degree-dependent polynomial-based reciprocally convex matrix inequality (RCMI) is proposed for obtaining less conservative stability criteria. Unlike previous RCMIs, the matrix inequality in this article produces a polynomial of any degree in the time-varying delay, which helps to reduce conservatism. In addition, to reduce the computational complexity caused by dealing with the negative definite of the high-degree terms, an improved lemma is presented. Applying the above matrix inequalities and improved negative definiteness condition helps to generate a more relaxed stability criterion for analyzing time-varying DNNs. Two examples are provided to illustrate this statement.