CONTROLLABILITY, OBSERVABILITY AND THE SOLUTION OF AX-XB=C Academic Article uri icon

abstract

  • A closed-form finite series representation of the unique solution X of the matrix equation AX - XB=C is developed. Using this representation, the image, kernel, and rank of X are related to the controllable and unobservable subspaces of the (A, C) and (C, B) pairs respectively. Bounds on the rank of X are obtainedin terms of the dimensions of these subspaces. In the case that C has unitary rank, an exact calculation of rank X is made. The generic rank of X with A, B fixed and C generic is evaluated. 1981.

published proceedings

  • LINEAR ALGEBRA AND ITS APPLICATIONS

altmetric score

  • 1

author list (cited authors)

  • DESOUZA, E., & BHATTACHARYYA, S. P.

citation count

  • 141

complete list of authors

  • DESOUZA, E||BHATTACHARYYA, SP

publication date

  • August 1981