Sylvester equation

The problem is here: Find X such that A*X+X*B-C (continuous time) or Find X such that A*X*B-C (discrete time)

function [X]=sylvester(A,B,C,flag)
// Generated by lmitool on Thu Feb 09 11:55:34 MET 1995
 Mbound = 1e3;abstol = 1e-10;reltol = 1e-10;
 nu = 10; maxiters = 100;
 options=[Mbound,abstol,nu,maxiters,reltol];
 ///////////DEFINE INITIAL GUESS AND PRELIMINARY CALCULATIONS BELOW
 [na,ma]=size(A);[nb,mb]=size(B)                                   
 if ma<>na|mb<>nb then error("invalid dimensions");end             
 X_init=zeros(ma,nb)                                               
 /////////// 
 XLIST0=list(X_init)
 XLIST=lmisolver(XLIST0,sylvester_eval,options)
 [X]=XLIST(:)

Evaluation function

  
 function [LME,LMI,OBJ]=sylvester_eval(XLIST)
 [X]=XLIST(:)
 /////////////////DEFINE LME, LMI and OBJ BELOW
 if flag=='c' then LME=A*X+X*B-C                                   
 else LME=A*X*B-C                                                  
 end                                                               
 LMI=[];OBJ=[]

Let's try a simple example with 3 states

A=[0,1,0;2,3,1;-1,-2,0];
B=[1,0;-2,1];
C=[1,2;0,1;1,-2];
[X]=sylvester(A,B,C,'c');
disp(X, 'X found is:')
disp(A*X+X*B-C ,'Check: A*X+X*B-C =')
 X found is:   
 
!   14.333333    3. !
! - 7.3333333  - 1. !
! - 1.3333333  - 1. !
 
 Check: A*X+X*B-C =   
 
   1.0D-14 *
 
! - 0.0888178    0. !
! - 0.2664535    0. !
!   0.           0. !