Abstract
We present a new algorithm for solving the Sylvester observer equation arising in the context of the Luenberger observer. The algorithm embodies two main computational phases: the solution of several independent equation systems and a series of matrix–matrix multiplications. The algorithm is, thus, well suited for parallel and high-performance computing. By reducing the coefficient matrix A to lower-Hessenberg form, one can implement the algorithm efficiently, with few floating-point operations and little workspace. The algorithm has been successfully implemented on a CRAY C90. A comparison, both theoretical and experimental, has been made with the well-known Hessenberg–Schur algorithm which solves an arbitrary Sylvester equation. Our theoretical analysis and experimental results confirm the superiority of the proposed algorithm, both in efficiency and speed, over the Hessenberg–Schur algorithm.
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