Abstract
We propose a new algorithm for block-wise solution of the generalized Sylvester-observer equation XA−FXE = GC, where the matrices A, E, and C are given, the matrices X, F, and G need to be computed, and matrix E may be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) into the observer-Hessenberg-triangular form. It is a natural generalization of the widely known observer-Hessenberg algorithm for the Sylvester-observer equation: XA−FX = GC, which arises in state estimation of a standard first-order state-space control system. An application of the proposed algorithm is made to state and velocity estimations of second-order control systems modeling a wide variety of vibrating structures. For dense un-structured data, the proposed algorithm is more efficient than the recently proposed SVD-based algorithm of the authors. Copyright © 2010 John Wiley & Sons, Ltd.
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