H∞ Kalman filtering for rectangular descriptor systems with unknown inputs

This paper considers H∞ filtering for rectangular descriptor systems with unknown inputs that affect both the system and the output. An optimal H∞ filter is developed based on the maximum likelihood descriptor Kalman filtering (DKF) method. The developed H∞ filter serves as a unified solution to solve H∞ and Kalman filtering for descriptor systems and standard systems with or without unknown inputs, which, however, may also suffer from computational complexity problem. Three computationally efficient alternatives to the developed H∞ filter are further proposed based on a novel matrix transformation and the recently proposed gain-covariance matrix (GCM) concept to remedy the computational problem. Simulation results are given to illustrate the usefulness of the proposed results.