Quantized fault-tolerant pinning control for finite-time H∞ synchronization of T-S fuzzy discrete Markovian-jump complex networks subject to heterogeneous delays

Abstract

This paper investigates the finite-time ℋ ∞ pinning synchronization problem for a class of T-S fuzzy discrete Markovian-jump complex networks (TSFDMCNs) influenced by heterogeneous delays. The evolution of system parameters follows the Markov jump process according to a transition probability matrix with partly unknown elements. Based on the system state output, quantized fault-tolerant pinning controller (QFTPC) is designed to overcome communication limitations and varying actuator fault. Besides, the asynchronous signal generated by the hidden Markov model is employed in controller to make full use of received information. A novel mode-dependent Lyapunov- Krasovskii functional (LKF) is established to guarantee the error system mean-square finite-time bounded with the prescribed ℋ ∞ performance. In order to reduce conservatism of derived results, an improved Wirtinger-based inequality technique is applied in considering both lower and upper bounds of different delay. Finally, simulation examples illustrate the effectiveness and meliority of the proposed theoretical methods.