Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters.

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis.