Optimal robust non-fragile Kalman-type recursive filtering with finite-step autocorrelated noises and multiple packet dropouts

In this paper, the optimal robust non-fragile Kalman-type recursive filtering problem is studied for a class of uncertain systems with finite-step autocorrelated measurement noises and multiple packet dropouts. The system state, measurement output and filter parameters are all subject to stochastic uncertainties or multiplicative noises, where the measurement noises are finite-step autocorrelated. When there exist multiple packet dropouts in the system output, the original system is converted into an auxiliary stochastic uncertain system by the augmentation of system states and measurements. The process noises and measurement noises of the auxiliary system are shown to be finite-step autocorrelated and cross-correlated. Then, a robust non-fragile Kalman-type recursive filter is designed that is optimal in the minimum-variance sense. The proposed filter is not only robust against the uncertainties in the system model and measurement model, but also non-fragile against the implementation error with the filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed method.