Input Estimation Over Frequency Region in Presence of Disturbances

A new formulation of the unknown input estimation problem in presence of unknown disturbances over a frequency region is presented. Necessary and sufficient conditions for existence of a solution are given and three estimation filters are given. The minimal attenuation is equal to the norm of a rational matrix over the frequency region. As a result, the minimum can be computed by solving linear matrix inequalities. An example is given, and the estimation with the proposed filters is illustrated by a numerical simulation and is compared with some state-of-the-art estimation filters.