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.