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How can I solve A*X + X*B = C equation for X? where A, B&C are 2*2 matrixes.

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HEmant kuralkar
HEmant kuralkar 2017-6-1
回答： Karan Gill 2017-6-5
A = [1 1;2 3] B= [5 6;7 8] C = [11 12;13 14] Syms X; Eqn = A*X + X*B == C; solve(Eqn,X); % I'm facing difficulties to define matrix X as syms

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采纳的回答

Steven Lord
Steven Lord 2017-6-1
If you're using release R2014a or later, use the sylvester function in MATLAB.
If you're using an older release but have access to Control System Toolbox, use the lyap function.

更多回答（2 个）

Andrei Bobrov
Andrei Bobrov 2017-6-1
>> A = [1 1;2 3];
B= [5 6;7 8];
C = [11 12;13 14];
X = reshape(sym('x',[4,1],'real'),2,[]);
v = A*X + X*B - C;
v = v(:);
f = matlabFunction(v,'Vars',{X});
x = fsolve(f,[1;1;1;1])
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
<stopping criteria details>
x =
2.1809
-0.1489
-0.2766
1.4043
>> X = reshape(x,2,[]);
>> v = A*X + X*B - C
v =
1.0e-14 *
-0.3553 -0.3553
-0.1776 -0.5329
>>
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Andrei Bobrov
Andrei Bobrov 2017-6-1
编辑：Andrei Bobrov 2017-6-1
Same
>> A = [1 1;2 3] ;
B= [5 6;7 8] ;
C = [11 12;13 14] ;
syms x1 y1 x2 y2
X = [x1 y1 ; x2 y2] ;
eqn = A*X+X*B == C ;
D = solve(eqn);
X = reshape(sym('x',[4,1],'real'),2,[]);
v = A*X + X*B - C;
v = v(:);
f = matlabFunction(v,'Vars',{X});
x = fsolve(f,[1;1;1;1]);
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
<stopping criteria details>
>> structfun(@double,D) - x
ans =
1.0e-14 *
0.6217
-0.4469
-0.4219
0.3775
>>

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Karan Gill
Karan Gill 2017-6-5
You can solve this with the symbolic toolbox if you declare "X" as a matrix:
>> X = sym('x%d',[2 2])
X =
[ x11, x12]
[ x21, x22]
Then solve as usual:
>> A = [1 1;2 3];
B= [5 6;7 8];
C = [11 12;13 14];
>> eqn = A*X + X*B == C
eqn =
[ 6*x11 + 7*x12 + x21 == 11, 6*x11 + 9*x12 + x22 == 12]
[ 2*x11 + 8*x21 + 7*x22 == 13, 2*x12 + 6*x21 + 11*x22 == 14]
>> sol = solve(eqn,X)
sol =
struct with fields:
x11: [1×1 sym]
x21: [1×1 sym]
x12: [1×1 sym]
x22: [1×1 sym]
>> solX = [sol.x11 sol.x12; sol.x21 sol.x22]
solX =
[ 205/94, -13/47]
[ -7/47, 66/47]
>> vpa(solX)
ans =
[ 2.1808510638297872340425531914894, -0.27659574468085106382978723404255]
[ -0.1489361702127659574468085106383, 1.4042553191489361702127659574468]

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