An Improved Stability Condition for Kalman Filtering with Bounded Markovian Packet Losses
It provides a less conservative stability condition for Kalman filtering under packet losses, benefiting control and estimation systems with unreliable communication.
The paper establishes a sufficient condition for peak-covariance stability of Kalman filtering with bounded Markovian packet losses, reformulated as an LMI feasibility problem, and demonstrates it is less conservative than existing results.
In this paper, we consider the peak-covariance stability of Kalman filtering subject to packet losses. The length of consecutive packet losses is governed by a time-homogeneous finite-state Markov chain. We establish a sufficient condition for peak-covariance stability and show that this stability check can be recast as a linear matrix inequality (LMI) feasibility problem. Comparing with the literature, the stability condition given in this paper is invariant with respect to similarity state transformations; moreover, our condition is proved to be less conservative than the existing results. Numerical examples are provided to demonstrate the effectiveness of our result.