Abstract :
We propose a new block algorithm for 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 could be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) to 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 estimation of second order control systems modeling a wide variety of vibrating structures. For dense un-structured data, the algorithm is more efficient than the recently proposed SVD-based algorithm of the authors, numerically reliable and heavily composed of Basic Linear Algebra Subprograms -Level 3 (BLAS 3) operations, which make it an ideal candidate for high-performance computing.
Keywords :
control system analysis; matrix algebra; observers; state-space methods; Sylvester matrix equation; block algorithm; dense unstructured data; first-order state-space control system; generalized Sylvester-observer equation; observer-Hessenberg-triangular form; orthogonal triplet decomposition; second order control systems; state estimation; vibrating systems; Control system synthesis; Control systems; Eigenvalues and eigenfunctions; Equations; Linear algebra; Linear systems; Mathematics; Matrix decomposition; Modeling; State estimation;
