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 equat...
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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 GRAY 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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