Optimal reduced-order observer-estimators

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Abstract
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 Author(s) Haddad, M.M. Florida Inst. of Technol., Melbourne, FL, USA Bernstein, D.S.