Global exponential synchronization of interval neural networks with mixed delays via delayed impulsive control

Fin-TS and Fix-TS on fractional quaternion delayed neural networks with uncertainty via establishing a new Caputo derivative inequality approach

This paper investigates the finite time synchronization (Fin-TS) and fixed time synchronization (Fix-TS) issues on Caputo quaternion delayed neural networks (QDNNs) with uncertainty. A new Caputo fractional differential inequality is constructed, then Fix-TS settling time of the positive definite function is estimated, which is very convenient to derive Fix-TS condition to Caputo QDNNs. By designing the appropriate self feedback and adaptive controllers, the algebraic discriminant conditions to achieve Fin-TS and Fix-TS on Caputo QDNNs are proposed based on quaternion direct method, Lyapunov stability theory, extended Cauchy Schwartz inequality, Jensen inequality. Finally, the correctness and validity of the presented results under the different orders are verified by two numerical examples.

Event-based master-slave synchronization of complex-valued neural networks via pinning impulsive control

This paper investigates the synchronization problem of complex-valued neural networks via event-triggered pinning impulsive control (ETPIC). A time-delayed pinning impulsive controller is proposed based on three levels of event-triggered conditions. By employing the Lyapunov functional method and differential inequality technique, sufficient delay-dependent synchronization criteria are derived under the proposed ETPIC scheme. The obtained result shows that synchronization of master and slave complex-valued neural networks can be achieved even if the sizes of delays exceed the length of intervals between any two consecutive impulsive instants determined by Lyapunov-based event-triggered conditions in the proposed control strategy. Moreover, the linear matrix inequality approach is utilized to exclude Zeno behavior. Numerical examples are provided to illustrate the effectiveness of the theoretical results.