Kalman Filtering for Discrete-Time Networked Control Systems with Incomplete Observations: A Dropping Over-Delayed Packets Approach

In this paper, with regards to discrete-time networked control systems with incomplete observations, a novel optimal linear estimator design is presented. Through a threshold-length buffer coupled to the estimator and a dropping over-delayed packet strategy, the packet arrival process is artificially limited to time pre-threshold at current moment. According to statistics and probability theory, we model the packet arrival probability subject to the choice of threshold. Based on linear matrix inequality (LMI) theorem and modified Riccati equation with packet arrival probability, with the existence of a critical bound of packet arrival rate, we can completely establish the relation between the filter convergence and the threshold-based packet arrival process as well as characterize the filter performance. Examples demonstrate the feasibility and practicability of the proposed method.