Non-Fragile $H_{∞ }$ Synchronization for Markov Jump Singularly Perturbed Coupled Neural Networks Subject to Double-Layer Switching Regulation

This work explores the $H_{infinity }$ synchronization issue for singularly perturbed coupled neural networks (SPCNNs) affected by both nonlinear constraints and gain uncertainties, in which a novel double-layer switching regulation containing Markov chain and persistent dwell-time switching regulation (PDTSR) is used. The first layer of switching regulation is the Markov chain to characterize the switching stochastic properties of the systems suffering from random component failures and sudden environmental disturbances. Meanwhile, PDTSR, as the second-layer switching regulation, is used to depict the variations in the transition probability of the aforementioned Markov chain. For systems under double-layer switching regulation, the purpose of the addressed issue is to design a mode-dependent synchronization controller for the network with the desired controller gains calculated by solving convex optimization problems. As such, new sufficient conditions are established to ensure that the synchronization error systems are mean-square exponentially stable with a specified level of the $H_{infinity }$ performance. Eventually, the solvability and validity of the proposed control scheme are illustrated through a numerical simulation.