Reduced-order observer for systems with piecewise constant inputs

The problem of reduced-order state estimators for systems with deterministic, i.e. known input is considered. Since below a certain order exact tracking of the state with reduced-order estimator is, in general, impossible, the approximation should take into account the class of expected inputs. In this paper a reduced-order estimator is designed for systems subjected to inputs consisting of set functions with varying amplitudes. The estimation error is required to be zero at steady state and its transient is minimized in the L2 sense. The optimal estimator is given explicitly and its structure is determined by three projection matrices.