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)?
1 view (last 30 days)
Show older comments
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).
Accepted Answer
MathWorks Support Team
on 27 Jun 2009
" 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.
0 Comments
More Answers (0)
See Also
Categories
Find more on Matrix Computations in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!