Robust estimator design using μ synthesis

H_∞ norm optimization and the structured singular value μ are used to design state estimators that are robust to noise and plant modeling errors. An H_∞ optimal estimator is derived as the solution to a minimax problem. In the suboptimal case, as an H_∞ norm constraint is removed, the minimax estimator approaches the steady-state Kalman filter. Robustness to plant modeling errors is achieved by minimizing a frequency-weighted H_∞-norm problem. The weighted H_∞ norm, μ, is an upper bound for μ, and therefore provides a sufficient condition for robust performance. The Kalman filter and μ estimator are compared using an example plant with modeling uncertainty. The μ estimator has slightly worse performance than the Kalman filter for the nominal plant model, but, unlike the Kalman filter, maintains its performance over the entire range of the modeling uncertainty