Co-existence of robust output-feedback synchronization and anti-synchronization of delayed discrete-time neural networks with its application

The problem of robust synchronization and anti-synchronization (S-AS) criteria for delayed discrete-time neural networks (NNs) is dealt in this paper via output-feedback control. Some new weighted summation inequalities are developed by combining the summation inequalities with reciprocal convex matrix inequality (RCMI) for handling the quadratic summation terms involved in the forward difference of the proposed Lyapunov–Krasovskii functional (LKF). Several less conservative delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to establish the S-AS criteria for the desired master–slave system model. Numerical examples with simulation results are explored using the time-domain and phase-plane approach; further, the comparative results are provided with existing literature to confirm the applicability and assurance of the derived theoretical results. In addition, network secure communication has been implemented by synchronization criteria, and the effectiveness of the application is verified via simulation results.