Finite-time synchronization of discontinuous fuzzy neural networks with mixed time-varying delays and impulsive disturbances

Abstract

In this paper, the finite-time synchronization issue is addressed for discontinuous fuzzy neural networks with mixed time-varying delays and impulsive disturbances. The dynamic impulsive gain about the impulsive moment is proposed as an alternative to the previous static impulsive gain. The time-varying impulsive gain can combine the synchronizing and desynchronizing impulses to directly observe their effects on the system, avoiding the classification discussion. In order to study the finite-time synchronization of the drive–response system, we obtain an equivalent system from the original fuzzy neural networks based on the concepts of Filippov solutions and differential inclusion theory. Furthermore, by constructing new Lyapunov functions that combine the 1-norm and the comparative system method, some algebraic sufficient conditions for the synchronization of the drive system and the response system in finite time are established, which are based on two types of novel non-chattering controllers. In addition, the parameters of the system itself can simply demonstrate the sufficient conditions that have been obtained her e, avoiding the time-consuming calculation of matrix inequalities. Moreover, the settling time estimation scheme have been established. Eventually, numerical examples are provided to demonstrate the effectiveness of the control scheme.

Keywords

• Finite-time synchronization
• Discontinuous fuzzy neural networks
• Discrete and distributed time-delays
• Impulsive disturbances