Inverse Laplace transform of a 4 by 4 matrix

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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

Accepted Answer

Sam Chak
Sam Chak on 22 Nov 2023
Since this is a linear dynamic system described in state-space, the output can be found using the dsolve() command.
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)
Gsol = struct with fields:
x: C1*(exp(-(t*(880740210851004153290091*((3^(1/2)*43740438401693126157487504478370365822531694805937937204624469331174935258419763369366273851571079352664988310139012389846237400821611425481… w: C1*(exp(-(t*(880740210851004153290091*((3^(1/2)*43740438401693126157487504478370365822531694805937937204624469331174935258419763369366273851571079352664988310139012389846237400821611425481… y: C1*(exp(-(t*(880740210851004153290091*((3^(1/2)*43740438401693126157487504478370365822531694805937937204624469331174935258419763369366273851571079352664988310139012389846237400821611425481… z: C3*exp(-(t*(880740210851004153290091*((3^(1/2)*437404384016931261574875044783703658225316948059379372046244693311749352584197633693662738515710793526649883101390123898462374008216114254819…
%% 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)
Psol = struct with fields:
x: (2245501681194912713180821901898316369833105182787823237505398159820541372242590057761026213554694888135433837660368384056135068619771591528250850247291290758676480000000000000000000000000… w: (2245501681194912713180821901898316369833105182787823237505398159820541372242590057761026213554694888135433837660368384056135068619771591528250850247291290758676480000000000000000000000000… y: (18429039118821823205910363600473469*(exp(-(t*(880740210851004153290091*((3^(1/2)*4374043840169312615748750447837036582253169480593793720462446933117493525841976336936627385157107935266498… z: (2245501681194912713180821901898316369833105182787823237505398159820541372242590057761026213554694888135433837660368384056135068619771591528250850247291290758676480000000000000000000000000…
Sam Chak
Sam Chak on 23 Nov 2023
Edited: Sam Chak on 23 Nov 2023
Hmm... This is strange. It looks complete on my machine. That's why I requested you to post exactly the same code and then hit the Run button . Let me check if I can the display completely from your side.
Walter Roberson
Walter Roberson on 23 Nov 2023
You might need to use the scroll-bars under the output expressions.

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More Answers (1)

Walter Roberson
Walter Roberson on 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
Walter Roberson
Walter Roberson on 22 Nov 2023
talks about converting state space to transfer function. You would then take the inverse laplace of the transfer function.
Sunday Aloke
Sunday Aloke on 22 Nov 2023
Yes, it's a state space matrix Please I am totally ignorant of the code to use. Sample of code will really help

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