A new block algorithm for full-rank solution of the Sylvester-observer equation

Abstract—A new block algorithm for computing a full rank solution of the Sylvester-observer equation arising in state estimation is proposed. The major Computational Kernels of this algorithm are (i) solutions of ordinary Sylvester equations, in which case each one of the matrices is of much smaller order than that of the system matrix and furthermore, this small matrix can be chosen arbitrarily, (ii) orthogonal reduction of small order matrices. There are numerically stable algorithms for performing these tasks. The algorithm is rich in Level 3 Basic Linear Algebra Subprograms (BLAS-3) computations and thus suitable for high performance computing. Furthermore, the results on numerical experiments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.