An algorithm for solving the matrix equationX = FXFT+S
Genshiro Kitagawa · International Journal of Control · 1977
A now algorithm for solving the matrix equation X = FXF T + S, which is important in the control system design, is presented in this paper. The algorithm is based on the QR algorithm for finding the eigenvalues of a matrix and works efficiently for large dimensional problems. A simple example is given to illustrate the algorithm. The method is also applicable to other types of equations such as the Lyapunov equation A T X + XA + B = 0.