Hybrid control strategy of delayed neural networks and its application to sampled-data systems: an impulsive-based bilateral looped-functional approach

In this work, the problem of hybrid control strategy for delayed neural networks is investigated via an impulsive-based bilateral looped-functional (IBBLF) approach. Firstly, a hybrid controller is introduced, which includes feedback control and impulsive control, and the feedback control plays a vital role in the case of impulsive perturbation. Secondly, an IBBLF is constructed to relax the requirement of positive definiteness and only satisfies it at the impulsive instants, which reduces the conservatism of the stability results. Thirdly, the construction of IBBLF takes full advantage of the state information on both the intervals $$z(t^{+}_k)$$ to z(t) and z(t) to $$z(t_{k+1})$$ , then combining with a proposed lemma, exponential stability criteria with less conservative are obtained. In addition, the obtained results are applied to nonlinear sampled-data systems. Finally, two numerical examples are presented to certify the effectiveness and superiority of the theoretical results.