Riccati Equation Solution Method for the Computation of the Solutions of X + A T X 1 A = Q and XA T X 1 A = Q †
Μαρία Αδάμ, Nicholas Assimakis, Grigoris Tziallas, Francesca Sanida · The Open Applied Informatics Journal · 2009
A test is developed for checking the existence of a finite number of solutions of the matrix equations X + A T X 1 A = Q and XA T X 1 A = Q, when A is a nonsingular matrix. An algebraic method for computing all the solutions of these matrix equations is proposed. The method is based on the algebraic solution of the corresponding discrete time Riccati equations. The number of solutions is also derived. The extreme solutions are computed as well.