H∞ stabilization problem for memristive neural networks with time-varying delays

This work explores memristive neural networks’ (MNNs) stability and stabilization problems by considering the time-varying delay and external disturbance. First, the MNNs were transformed into a tractable model by defining the logical switched functions, paving the way to utilize the robust analysis method for the associated connection weights. Second, by proposing a new Lyapunov–Krasovskii functional constructed by the delay-partitioning approach and the free weight matrices, the exponential stability (ES) problem of the transformed MNNs model is investigated. Third, the state feedback controller's design scheme is devised to ensure the ES of the overall closed-loop system with a prescribed H_∞ disturbance attenuation performance level γ. The results are formed in terms of linear matrix inequalities. Finally, two suitable examples express the efficacy of the proposed results.