Pinning exponential synchronization for inertial coupled neural networks via adaptive aperiodically intermittent control under directed topology.

• A non-reduced order method is adopted to avoid the two-dimensional problem deriving from the reduced-order method [12,13,17–20], a Lyapunov-Krasovskii functional is constructed to analyze synchronization issues of ICNNs. • Adaptive aperiodically intermittent controller is developed to achieve pinning exponential synchronization of ICNNs under more general directed graph. The asymmetric property of the associated Laplacian matrix, the synchronization problems of ICNNs are challenging. • By Lyapunov stability theory, matrix decomposition theory as well as M-matrix theory, synchronization criteria in terms of LMIs are established, which are dependent on the control ratio and the topology of the network. This article is mainly focused on investigating pinning exponential synchronization of inertial coupled neural networks (ICNNs) under different directed topologies. The traditional method of variable substitution is removed and replaced by non-reduced order method to investigate the dynamical behavior of second-order coupled system. Additionally, by constructing Lyapunov-Krasovskii functional and utilizing matrix decomposition theory as well as M-matrix theory, an adaptive aperiodically intermittent controller is introduced to derive several improved sufficient criteria based on linear matrix inequalities (LMIs). Finally, some examples with numerical simulation are exhibited to confirm the availability of the theoretical results. [ABSTRACT FROM AUTHOR]