Use the Matlab function EXPM()

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ahmed dalatony
ahmed dalatony 2019-4-10
评论： Rik 2022-2-9
Given the attached State Equation and initial condition:
(a) Use the Matlab function EXPM() to compute a numerical representation for the Matrix Exponential. You will need to establish a time vector that has an appropriate time resolution and an appropriate time duration to numerically capture the time dependency of each element in the matrix exponential.
(b) Use the Symbolic Toolbox with the EXPM() function in Matlab to generate a
symbolic representation for the Matrix Exponential.
(c) Numerically evaluate the symbolic representation from (b) using the same time
vector from (a).
(d) Generate an analytic representation for the Matrix Exponential using Laplace
Transforms. You should do this problem by hand, but you are welcome to use
the Symbolic Toolbox in Matlab to check your result.
(e) Numerically evaluate the symbolic representation from (d) using the same time
vector from (a).
(f) Use Matlab to generate a plot of all elements in the Matrix Exponential. In this
plot, you must compare the numerical results from (a), (c), and (e). Your subplots
must be properly annotated and clearly show all three curves in the comparison.
(Hint: If you did the problem correctly, the numerical results should be identical.
If you plot three identical curves on top of each other, you will only be able to
see the last one plotted. You need to show all three identical curves without
  2 个评论
Rik
Rik 2022-2-9
Regarding the flag by @ahmed dalatony ("delete the the content, please"):
Why do you want to delete the content?
Use the Matlab function EXPM()
Given the attached State Equation and initial condition:
(a) Use the Matlab function EXPM() to compute a numerical representation for the Matrix Exponential. You will need to establish a time vector that has an appropriate time resolution and an appropriate time duration to numerically capture the time dependency of each element in the matrix exponential.
(b) Use the Symbolic Toolbox with the EXPM() function in Matlab to generate a
symbolic representation for the Matrix Exponential.
(c) Numerically evaluate the symbolic representation from (b) using the same time
vector from (a).
(d) Generate an analytic representation for the Matrix Exponential using Laplace
Transforms. You should do this problem by hand, but you are welcome to use
the Symbolic Toolbox in Matlab to check your result.
(e) Numerically evaluate the symbolic representation from (d) using the same time
vector from (a).
(f) Use Matlab to generate a plot of all elements in the Matrix Exponential. In this
plot, you must compare the numerical results from (a), (c), and (e). Your subplots
must be properly annotated and clearly show all three curves in the comparison.
(Hint: If you did the problem correctly, the numerical results should be identical.
If you plot three identical curves on top of each other, you will only be able to
see the last one plotted. You need to show all three identical curves without

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回答（1 个）

David Wilson
David Wilson 2019-4-10
I'll get you going on part (b):
syms t positive
A = sym([0,-5;1,-2]);
Phi = expm(A*t)

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