Optimal input design for robust H2 deconvolution filtering

Deconvolution filtering where the system and noise dynamics are obtained by parametric system identification is considered. Consistent with standard identification methods, ellipsoidal uncertainty in the estimated parameters is considered. Three problems are considered: 1) Computation of the worst case H2 performance of a given deconvolution filter in this uncertainty set. 2) Design of a filter which minimizes the worst case H2 performance in this uncertainty set. 3) Input design for the identification experiment, subject to a limited input power budget, such that the filter in 2) gives the smallest possible worst-case H2 performance. It is shown that there are convex relaxations of the optimization problems corresponding to 1) and 2) while the third problem can be treated via iterating between two convex optimization problems.