Optimal Filter for Sampled-data Systems with Multi-channel Markovian Packet Losses and Transmission Delay

This paper investigates the optimal filtering for the sampled-data systems with multiple Markovian packet losses and observation delays. A new Markov chain is introduced to tackle the packet loss phenomenon, and the reorganization observation technique is employed to deal with the transmission delay, by which the original sampled system is transformed into a sampled-data delay-free jumping parameter system. Based on the converted system, the optimal Markov jump linear filter is designed by the completion method and the stochastic approximation method, where the filter gains are given in terms of a piecewise continuous Riccati equation. Furthermore, the convergence analysis is supplied for the optimal filtering, and the stationary filter is obtained by solving a type of algebraic Riccati equation. Finally, an illustrative example is given to show the efficiency of the proposed filters.