H∞ fixed-lag smoothing and prediction for linear continous-time systems

Abstract

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 H 2 estimation 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.