Page 198 - Numerical Analysis Using MATLAB and Excel

Computation of the State Transition Matrix

a – a = e t –
1
0
a = te t –
1
Simultaneous solution of the last two equations yields

t –
a = e + te t –
0
(5.154)
a = te t –
1
4. By substitution of (5.154) into (5.153), we obtain

t –
e At = ( e + te ) t – 1 0 + te t – – 1 0 = e At = e t – 0 (5.155)
0 1 2 – 1 2te t – e t –

We can use the MATLAB eig(x) function to find the eigenvalues of an n × n matrix. To find out
how it is used, we invoke the help eig command.

We will first use MATLAB to verify the values of the eigenvalues found in Examples 5.16 through
5.18, and we will briefly discuss eigenvectors on the next section.
For Example 5.16:

A= [−2 1; 0 −1]; lambda=eig(A)

lambda =
-2
-1
For Example 5.17:

B = [5 7 −5; 0 4 −1; 2 8 −3]; lambda=eig(B)

lambda =
1.0000
3.0000
2.0000
For Example 5.18:

C = [−1 0; 2 −1]; lambda=eig(C)

lambda =
-1
-1

Numerical Analysis Using MATLAB® and Excel®, Third Edition 5−37

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