Delay-distribution-dependent state estimation for neural networks under stochastic communication protocol with uncertain transition probabilities

In this paper, the protocol-based remote state estimation problem is considered for a kind of delayed artificial neural networks. The random time-varying delays fall into certain intervals with known probability distributions. For the sake of reducing the data collisions in communication channel from the sensors to the estimator, the stochastic communication protocol (SCP) is employed to decide which sensor is allowed to transmit its data to the remote estimator through the channel at each fixed instant. The scheduling principle of the SCP is governed by a Markov chain whose transition probability is allowed to be uncertain so as to reflect the possible imprecision when implementing the SCP. Through a combination of Lyapunov-Krasovskii functional method and the stochastic analysis technique, a sufficient criterion is obtained for the existence of the desired remote state estimator ensuring that the corresponding augmented estimation error dynamics is asymptotically stable with a prescribed H∞ performance index. Furthermore, the estimator parameter is acquired by solving a convex optimization problem. Finally, the validity of the established theoretical results is demonstrated via a numerical simulation example.