Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers.

Abstract

This paper considers the finite-time cluster synchronization (FTCS) of coupled fuzzy cellular neural networks (FCNNs) with Markovian switching topology, discontinuous activation functions, proportional leakage, and time-varying unbounded delays. Novel quantized controllers without the sign function are designed to avoid the chattering and save communication resources. Under the framework of Filippov solution, several sufficient conditions are derived to guarantee the FTCS by constructing new Lyapunov-Krasovskii functionals and utilizing M-matrix methods. The new analytical techniques skillfully overcome the difficulties caused by time-varying delays and cope with the uncertainties of both Filippov solution and Markov jumping, which enable us determine the settling time explicitly. Numerical simulations demonstrate the effectiveness of the theoretical analysis.