Event-triggered state estimation for recurrent neural networks with unknown time-varying delays

We consider the problem of event-triggered state estimation for recurrent neural networks subject to unknown time-varying delays by proposing a robust dynamic event-triggered state observer. A method based on a novel state observer and a dynamic event-triggered mechanism (ETM) is proposed to provide robust state estimation of the delayed recurrent neural networks. The significance of the new dynamic ETM is that it helps to reduce unnecessary transmissions from the sensors to the observer. A sufficient condition for the existence of the dynamic event-triggered state observer in terms of a convex optimization problem is proposed based on Lyapunov theory combined with free-weighting matrix technique and some useful inequalities such as Wirtinger-based integral inequality, Cauchy matrix inequality and reciprocally convex combination inequality. The effectiveness of the proposed estimation method is demonstrated by two numerical examples and simulation results. In contrast to the event-triggered state estimation methods currently available in the literature, which require that the time delays are constant or unknown time-varying but must be differentiable and event-triggered conditions depend on continuous supervisions, the one in this article only requires the information of upper and lower bounds of the unknown time-varying delays and the event-triggered conditions depend on discrete supervisions, which provides more practicality and potential saving in network bandwidth.