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Inverse Laplace transform of a 4 by 4 matrix
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Sunday Aloke
il 22 Nov 2023
Commentato: Walter Roberson
il 23 Nov 2023
Please house, I need help to output the inverse Laplace transform of the 4 by 4 matrix attached below. I will be grateful for your assistance. Thanks
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Sam Chak
il 22 Nov 2023
Since this is a linear dynamic system described in state-space, the output can be found using the dsolve() command.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1546377/image.jpeg)
syms w(t) x(t) y(t) z(t)
%% State equations
eqns = [diff(w,t) == - 0.00022074*w + 0*x - 0.321386*y + 0.0000004924*z,
diff(x,t) == 0.00012074*w - 0.187744*x + 0.321385*y + 0*z,
diff(y,t) == 0*w + 0.187644*x - 0.321215*y + 0*z,
diff(z,t) == 0*w + 0*x + 0.318725*y - 0.0001005*z];
%% General solution (if initial condition is unknown)
Gsol = dsolve(eqns, 'MaxDegree', 4)
%% Particular solution (if initial condition is known)
cond = [w(0) == 1,
x(0) == 0,
y(0) == 0,
z(0) == 0];
Psol = dsolve(eqns, cond, 'MaxDegree', 4)
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Walter Roberson
il 22 Nov 2023
inverse laplace of a constant is dirac delta times the constant, so just multiply the matrix by dirac delta function.
Note that if your A is the A of a state space representation then you would have a completely different answer, and would need the other state space matrices as well
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Walter Roberson
il 22 Nov 2023
https://lpsa.swarthmore.edu/Representations/SysRepTransformations/TF2SS.html
talks about converting state space to transfer function. You would then take the inverse laplace of the transfer function.
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