Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen‐Grossberg–type neural networks
Chaouki Aouiti, El Abed Assali · International Journal of Adaptive Control and Signal Processing · 2019
Summary In this paper, without transforming the original inertial neural networks into the first‐order differential equation by some variable substitutions, time‐varying delays are introduced into inertial Cohen‐Grossberg–type networks and the existence, the uniqueness, and the asymptotic stability and synchronisation for the neural networks are investigated. Firstly, the existence of a unique equilibrium point is proved by using nonlinear Lipschitz measure method. Second, by finding a new Lyapunov‐Krasovskii functional, some sufficient conditions are derived to ensure the asymptotic stability, the asymptotic synchronization, and the asymptotic adaptive synchronization. The results of this paper are new and they complete previously known results. We illustrate the effectiveness of the approach through a few examples.