Novel Lebesgue-integral-based approach to improved results for neural networks with additive time-varying delay components. Issue 16 (November 2017) - Zeng, Deqiang; Zhang, Ruimei; Zhong, Shouming; Yang, Guowu; Yu, Yongbin; Shi, Kaibo
Abstract: In this paper, we propose a novel Lebesgue-integral-based approach to investigate the stability for neural networks with additive time-varying delay components. Based on the Lebesgue integral theory, a new Lyapunov–Krasovskii functional (LKF), which involves Lebesgue integral terms, is constructed, and the corresponding stability theorem is derived. More information on the neuron activation functions and fewer matrix variables are involved in the constructed LKF. Then, on the basis of the above method, an improved stability criterion is developed. Compared with the existing results, the derived stability condition is with less conservatism and computational burden. Moreover, the obtained criterion is extended to study the system with a single time-varying delay. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.