Mixed H-2/H-infinity filtering

In paper we consider the problem of finding a filter or estimator that minimizes a mixed H-2/H-infinity filtering cost on the transfer matrix from a given noise input to the filtering error subject to an H-infinity constraint on the transfer matrix from a second noise input to the filtering error, This problem can be interpreted and motivated in many different ways; for instance, as a problem of optimal filtering in the presence of noise with fixed and known spectral characteristics subject to a bound on the filtering error due to a second noise source whose spectral characteristics are unknown, It is shown that one can come arbitrarily close to the optimal mixed H-2/H-infinity filtering cost using a standard Kalman-Luenberger estimator. Moreover, the problem of finding suitable Kalman-Luenberger estimator gains can be converted into a convex optimization problem involving affine symmetric matrix inequalities.