Stabilization and Energy Consumption Estimation of Discontinuous Fuzzy Inertial CGNNs via Saturation Function Approach

In this article, finite/fixed-time stabilization and energy consumption estimation of a class of discontinuous fuzzy inertial Cohen-Grossberg neural networks (CGNNs) are considered. The saturation function is utilized to design the control laws, which is different from the previous ones with the sign function since the saturation function is continuous and can reduce the chattering phenomenon. By using the Lyapunov method, comparison principle, and differential inequality theory, the finite/fixed-time stabilization is analyzed by analyzing the state variables inside and outside the unit spherical area, which is different from the direct calculation method using finite/fixed-time stability lemmas. Detailed analyses show the differences in the estimations of the settling time between the initial values inside and outside of the unit spherical area. The energy consumption is also estimated when the finite/fixed-time stabilization is achieved under the designed controller, which is discussed for the first time in the inertial networks. Finally, the validity of the theoretical results is demonstrated by a typical numerical example.