Remote Estimator Design for Time-Delay Neural Networks Using Communication State Information

This paper investigates the estimator design for the neural networks, where distributed delays and imperfect measurements are included. A randomly occurred neuron-dependent nonlinearity is used to describe the uncertain measurements disturbed by neurons. The measurements are transmitted over multiple transmission channels, and Markov chains are introduced to model packet dropouts of these channels. A one-to-one map is constructed to transform $m$ independent Markov chains to an augmented one to facilitate system analysis. A new variable called channel state is defined based on the cases of packet dropouts, and the channel-state-dependent estimator is designed to trade off between the number and the performance of the estimator. Sufficient conditions are established to guarantee that the augmented system is stochastically stable and satisfies the strict $(Q, S, R)-\gamma -$ dissipativity. The estimator gains are derived using linear matrix methods. Finally, an example is applied to illustrate the effectiveness of the developed methods.