Design of H-infinity multi-step predictor for descriptor systems

Based on the method of innovation re-organization and the theory of Kalman filtering in Krein space, a sufficient and necessary condition for the existence of an H-infinity multi-step prediction for descriptor systems is given for the first time and a simple computation method is derived in this paper. Firstly, the H-infinity multi-step prediction problem for descriptor system is converted into a Krein space H₂ estimation problem with current and delayed measurements. Then, the latter one is solved by introducing a re-organization innovation sequence. The H-infmity predictor is thus computed by performing two Riccati equations that are with the same dimensions as a transformed system, and the usually used augmentation method for systems with delayed measurements is avoided. Finally, numerical example shows that the calculation burden of the descriptor systems H-infinity multi-step predictor based on re-organization innovation method is lighter than the one based on the method of system augmentation.