Bounded real lemma and H∞ control for BAM neural networks with unbounded time-varying delays

This article investigates the exponential $H_{\infty }$ control issue of bidirectional associative memory neural network (BAMNN) with unbounded time-varying delays. A bounded real lemma (BRL) is first established via a direct method, which is on the basis of the solutions of BAMNN. Second, based on the obtained BRL, the state feedback controller is designed to guarantee the global exponential stability of the resulting closed-loop BAMNN with an $H_{\infty }$ performance index. Since no Lyapunov–Krasovskii functionals is constructed in the proposed method, the computation burden and complexity are reduced. Lastly, the effectiveness of the theoretical results is illustrated through two numerical examples.