Robust synchronization of uncertain Markovian jumping complex interconnected neural networks via adaptive fault-tolerant control

This article inspects the problem of robust synchronization for uncertain Markovian jumping complex interconnected neural networks with randomly occurring uncertainties and time delays. The uncertainties considered here occur randomly and are assumed to follow certain mutually uncorrelated Bernoulli distributed white noise sequences. The presence of sensor faults may cause degradation or even instability of the entire network. Therefore, control laws are designed with sensor faults to ensure the controlled synchronization of the complex interconnected neural networks. Three types of fault-tolerant controls are designed based on the Lyapunov stability theory and adaptive schemes which include passive and adaptive fault-tolerant control laws. By constructing a new Lyapunov-Krasovskii functional (LKF) and by using Jensen’s inequality with a free-weighting matrix approach, some new delay-dependent synchronization criteria are obtained in terms of linear matrix inequalities (LMIs). By using the Lyapunov stability theory, the existence condition for the adaptive controller that guarantees the robust mean-square synchronization of complex interconnected neural networks in terms of LMIs are derived. Finally, a numerical example is presented to demonstrate the performance of the developed approach.