Stability Analysis of Delayed Neural Networks via Composite-Matrix-Based Integral Inequality

Abstract

This paper revisits the problem of stability analyses for neural networks with time-varying delay. A composite-matrix-based integral inequality (CMBII) is presented, which takes the delay derivative into account. In this case, the coupling information can be fully captured in integral inequalities with the delay derivative. Based on a CMBII, a new stability criterion is derived for neural networks with time-varying delay. The effectiveness of this method is verified by a numerical example.

Novel Robust Stability Criteria for Lur’e Systems with Time-Varying Delay

“…If the linear matrix inequalities (10) and (11) are satisfied, then it follows that Vc (t) + Vb (t) < −ϵ 2 ∥x(t)∥ 2 for a sufficiently small scalar ϵ 2 > 0. To summarize, there exists a scalar…”

“…Numerous scholars have conducted in-depth studies on various aspects of Lur'e systems [1][2][3][4][5][6][7][8][9]. On the other hand, time delay is a prevalent phenomenon that arises during the implementation process of actual systems [10][11][12]. The presence of time delay can significantly impact a system's performance and efficiency during normal operation, potentially leading to performance deterioration or even system collapse [13][14][15][16][17][18].…”

Stability Analysis of Linear Time-Varying Delay Systems via a Novel Augmented Variable Approach

“…This analysis helps pre-emptively predict and mitigate potential issues caused by time delays and provides crucial insights for developing effective control strategies and optimizing system designs. Currently, research on time-delay systems has achieved numerous advancements and breakthroughs, laying a solid foundation for addressing more complex time-delay issues and paving new paths for future technological development and innovation [2][3][4][5][6][7][8][9][10].…”