Information filtering for time-delay systems

This paper presents the information filter, which is developed in filtered forms, for time-delay systems which include continuous-time case and discrete-time case. By introducing delay-free observation, the optimal filtering problems for time-delay systems can be converted into multiple steps prediction problems for delay-free systems. Then, the recursive forms for optimal filter are given via innovation approach in Hilbert space. Furthermore, the information filter in Riccati recursions can be derived by using the matrix inversion Lemma to optimal filtering formulas. Finally, the distributed Kalman filter for time-delay systems is designed based on information filter developed.