State Estimation for Periodic Neural Networks With Uncertain Weight Matrices and Markovian Jump Channel States

This paper studies the state estimator design for periodic neural networks, where stochastic weight matrices <inline-formula> <tex-math notation="LaTeX">$ {B(k)}$ </tex-math></inline-formula> and packet dropouts are considered. The stochastic variables, which may influence each other, are introduced to describe uncertainties of weight matrices. In order to model the time-varying conditions of the communication channel, a Markov chain is employed to study the jumping cases of the stochastic properties of the packet dropouts (i.e., Bernoulli process with jumping means and variances being used to handle the packet dropouts). A state estimator is constructed such that the augmented system is stochastically stable and satisfies the <inline-formula> <tex-math notation="LaTeX">$ {H_{\infty }}$ </tex-math></inline-formula> performance. The estimator parameters are derived by means of the linear matrix inequalities method. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.