In this paper, we study the problem of global exponential stability for impulsive cellular neural networks with time-varying delays and supremums. Using Young's inequality and Lyapunov-like functions, new stability criteria are proved. Because supremums and impulses are relevant in various contexts, including problems in the theory of automatic control, our results can be applied in the qualitative investigations of many practical problems of diverse interest.

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In this paper, the problem of global exponential stability for impulsive cellular neural networks with time-varying delays and supremums over a past interval of time is studied. The impulses are realized at fixed moments of time and can be considered as a control. We establish several stability criteria by employing Lyapunov functions and the Razumikhin technique. These results can easily be used to design and verify globally stable networks.

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The present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen–Grossberg-type with reaction–diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based on the Lyapunov functions technique and Poincarѐ-type inequality some new global stability criteria are also proposed in our research. In addition, we consider the case when the impulsive jumps are not realized at fixed instants. Instead, we investigate a system under variable impulsive perturbations. Finally, examples are given to demonstrate the efficiency and applicability of the obtained results.