A frequency domain approach to the problems of H∞-minimum error state estimation and deconvolution

The properties of the minimum H_∞-norm filtering estimation error are investigated, and the relation between the optimal estimator and the equalizing solution to the standard H _∞-minimization problem is discussed. The optimal estimation method is applied in the multivariable deconvolution problem. A simple deconvolution filter of minimum order which minimizes the H _∞-norm of the deconvolution error is obtained. The proposed methods of optimal estimation and deconvolution are useful in cases where the statistics of the disturbance and the noise signals is not completely known, or in cases where it is required to minimize the maximum singular value of the estimation, or the deconvolution, error problem