Finite-Time Synchronization of Memristive Neural Networks with Proportional Delay

The problem of finite-time synchronization for memristive neural networks (MNNs) with proportional delay is considered. Since proportional delay is unbounded and different from infinite-time distributed delay, the classical finite-time analytical techniques are not applicable anymore. First, a discontinuous state feedback controller is designed such that the delayed MNNs achieve drive-response synchronization in a finite settling time. By using Filippov solution and Lyapunov functional method, sufficient conditions are derived. It is shown that, though the proportional delay is unbounded, complete synchronization can still be realized and the settling time can be explicitly estimated. Second, a special adaptive controller is designed for the finite-time problem in order to reduce the control gains. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.