Master–Slave Synchronization for Fuzzy Markovian Jump Complex Dynamical Networks with Coupling Delay Via Fault-Tolerant Control

This study addresses the challenge of synchronizing master and slave systems in complex dynamic networks using Takagi-Sugeno (T-S) fuzzy Markovian jump models, with the presence of coupling delays. To enhance synchronization robustness, fault-tolerant control mechanisms are implemented. State feedback controller is converted to fault-tolerant control and control gain matrices are derived to improve system stability in the presence of faults. Using Lyapunov-krasovskii functional and Linear Matrix Inequalities (LMIs), this study establishes precise stability proofs and analytical constraints to ensure stochastic mean-square stability. The use of LMIs enables the systematic design of fault-tolerant controllers and provides a formal framework for handling faults while maintaining system performance. Moreover, numerical simulations using a MATLAB LMI toolbox validate the effectiveness of the proposed fault-tolerant control strategy under various fault scenarios, highlighting its practical applicability in complex dynamical networks.