A new numerical solution of X = A_{1}X + XA_{2} + D, X(0) = C
A. Barraud · IEEE Transactions on Automatic Control · 1977
Another numerical solution of the general matrix differential equation\circ{X}=A_{1}X+XA_{2}+D, X(0)=Cfor X is considered without any stability condition for A1and A2. Like Davison's method, the proposed algorithm requires only some n2words of memory andn_{3multiplications wheren=\max(n_{1},n_{2})andA \in R^{n_{1} \times n_{1}},A_{2} \in R^{n_{2} \times n_{2}}. This new approach is well suited to solve large and possibly unstable systems. We take the opportunity to run the differential equation for various D. A very efficient technique follows to design the so-called receding horizon control problem.