H-infinity deconvolution filtering: A Krein space approach in state-space setting

This note is concerned with the H-infinity deconvolution filtering problem for linear time-varying discretetime systems described by state space models. The H-infinity deconvolution filter is derived by proposing a new approach in Krein space. With the new approach, it is clearly shown that the central deconvolution filter in an H-infinity setting is the same as the one in an H2 setting associated with one constructed stochastic state-space model. This insight allows us to calculate the complicated H-infinity deconvolution filter in an intuitive and simple way. The deconvolution filter is calculated by performing Riccati equation with the same order as that of the original system. © 2009 Editorial Board of Control Theory and Applications, South China University of Technology and Springer-Verlag GmbH.