MATLAB: MuPAD unable to get the expected representation

Question

Hi,

When I open MuPAD Notebook and type the following commands:

Ac := matrix([[0,1,0], [0,0,1], [0,0,0]]):
Dc := matrix([0,0,1]):
expre1 := exp((tk-tau)*Ac)*Dc:
expre2 := expre1*q*expre1':
Q := int(expre2, tau = tk-T..tk):
Simplify(Q)

to calculate the matrix Q, the result returned is an integral representation.

How to get the following expected results by using MuPAD,

Q(1,1) = (T^5*q)/20
Q(1,2) = (T^4*q)/8
Q(1,3) = (T^3*q)/6
Q(2,1) = (T^4*q)/8
Q(2,2) = (T^3*q)/3
Q(2,3) = (T^2*q)/2
Q(3,1) = (T^3*q)/6
Q(3,2) = (T^2*q)/2
Q(3,3) = T*q

Thanks in advance.

Answer 1

In MuPAD, exp() is not the matrix exponential; see http://www.mathworks.com/help/symbolic/mupad_ref/exp.html and http://www.mathworks.com/help/symbolic/mupad_ref/numeric-expmatrix.html