H_∞Fixed-Lag Smoothing and Prediction for Linear Continous-Time Systems

This paper addresses the H∞fixed-lag smoothing and prediction problems for linear continuous-time systems. We first present a solution to the optimal H2estimation problem for linear continuous-time systems with instantaneous and delayed measurements, It is then shown that the H∞fixed-lag smoothing and prediction problems can be converted to the latter problem in Krein space. Therefore, the H2estimation is extended to give conditions on the existence of a H∞fixed-lag smoother and predictor based on innovation analysis and projection in Krein space and a solution for H∞smoother or predictor is given in terms of a Riccati differential equation and matrix differential equations.