Page 410 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 410
CHAP. 71 STATE SPACE ANALYSIS
Then by Eq. (7.35) we obtain
= ~;,{(zI - A)-'z)
From the above results we note that when the eigenvalues of A are all distinct, the spectral
decomposition method is computationally the most efficient method of evaluating An.
7.24. Find An for
The characteristic polynomial c(A) of A is
5A + + = (A - l)(A - $1
4
Thus, the eigenvalues of A are A, = 1 and A, = 4, and by Eq. (7.33) we have
1 1 3
2
A
E2= - - ( A -
(
A2 -4 5 - 1 2
Thus, by Eq. (7.34) we obtain
