A well-known method by Anderson and Moore for optimal quadratic feedback design with guaranteed convergence rate for linear time-invariant systems is generalized to linear complex-valued time-varying systems and convergence rates. The resulting method is applied to observer design and illustrated by solving the problem of flux estimation in induction machines. A pre-assigned time-varying convergence rate is shown to improve the observer's transients in comparison with a constant one. The suggested design technique can be readily utilized for nonlinear state-affine systems