Optimal reduced-order observer-estimators

A unified approach to designing reduced-order observer-estimators is presented. Specifically, an attempt is made to design a reduced-order estimator satisfying an observation constraint which involves a prespecified, possibly unstable subspace of the system dynamics and which also yields reduced-order estimates of the remaining subspace. The results are obtained by merging the optimal projection approach to reduced-order estimation of D.S. Bernstein and D.C. Hyland (IEEE Trans. Autom. Control, vol.AC-30, p.583-5, 1985) with the subspace-observer results of the authors (Proc. IEEE Conf. on Decision and Control, p.2364-6, Dec. 1988). A salient feature of this theory is the treatment of unstable dynamics within reduced-order stable-estimation theory. In contrast to the standard full-order estimation problem involving a single algebraic Riccati equation, the solution to the reduced-order observer-estimator problem involves an algebraic system of four equations consisting of one modified Riccati equation and three modified Lyapunov equations coupled by two distinct oblique projections