\(H_\infty \) State Estimation for Round-Robin Protocol-Based Markovian Jumping Neural Networks with Mixed Time Delays

This paper discusses the \(H_\infty \) state estimation issue in regard to Markovian jumping neural networks (MJNNs) under the scheduling of the Round-Robin protocol (RRP). The model takes into account mixed time-delays, sensor nonlinearities and exogenous disturbances, making it relatively general and comprehensive. The transmission of MJNNs signals invoked a communication scheme in which the RRP is used for the data transmissions in order to avoid undesirable data collisions. Protocol-dependent state estimator modeling of a hybrid switching system with mixed time delays and disturbances is designed for the first time to achieve asymptotic tracing for the neuron state. Using the Lyapunov stability theory and several asymptotic methods, sufficient conditions for guaranteeing the asymptotic stability of the state estimation are established under the constraint of \(H_\infty \) performance. By employing a combination of matrix analysis techniques, the estimator gain matrices are calculated by the feasible solutions to the linear matrix inequalities (LMIs). Finally, a numerical example and related simulations demonstrate the validity of the proposed model.