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 H₂ estimation 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 H₂ estimation is extended to give conditions on the existence of 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.