Linear-quadratic optimal time-varying observers with time-varying guaranteed convergence rate

A well-known method by Anderson and Moore for optimal quadratic feedback design with guaranteed constant convergence rate for linear time-invariant systems is generalised to linear complex-valued time-varying systems and time-varying convergence rates. The resulting method is readily applicable to observer design for state-affine systems and unifies methods developed there with the classical quadratic optimal state estimation and control. A pre-assigned time-varying convergence rate is shown to significantly improve the observer's transients in comparison with a constant one being employed for flux estimation in induction machines.