Robust H2 estimation using the Popov-Tsypkin multiplier

This paper considers the design of robust, finite-horizon and infinite-horizon H₂ estimators based on multiplier theory (which is intimately related to the mixed structure singular value). Specifically, the Popov-Tsypkin multiplier is used to develop a novel upper bound on a finite-horizon, cost function for the assumed uncertainty set. The results are then applied to develop design equations for robust H₂ estimation which collapse to the standard Kalman filter design equations if the uncertainty is absent. The robust design equations are complex and possible solution approaches are discussed. Robust estimation using the Popov-Tsypkin multiplier is illustrated by using a parameter optimization approach (in particular, a zero-prediction, continuation algorithm) to design a robust filter for an infinite-horizon H₂ cost function