How do I solve the matrix equation A*M + M*B = C for M in terms of A , B and C using the Robust Control Toolbox 2.0.9 (R13)?

I would like to solve the matrix equation A*M + M*B = C for M in terms of A , B and C using the Robust Control Toolbox 2.0.9 (R13).

Answer 1

[MathWorks Support Team]

" A*M + M*B = C " can be solved using the LYAPKR function. This function is a part of Robust Control Toolbox 2.0.9. Below is a short description of the function that was found by typing the following at the command prompt:

   help LYAPKR

LYAPKR Lyapunov/Sylvester equation solver (Kronecker product approach).

   [X] = LYAPKR(A,B,C) produces the solution of a Lyapunov or Sylvester equation

        The algorithm is simply the Kronecker product of a special

        kind, i.e :

          A1*X*B1 + A2*X*B2 + A3*X*B3 + ... = Ck

          The solution is

          [KRON(A1,B1') + KRON(A2,B2') + ... ] * S[X] = S(Ck)

          For the Lyapunov or Sylvester equation :

              A1 = A,  B1 = I,  A2 = I, B2 = B,  Ck = -C.

         such that :  A * X + X * B + C = 0

This system of equation is not solved using any function in PDE toolbox.