Page 413 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 413
STATE SPACE ANALYSIS [CHAP. 7
Cayley-Hamilton theorem, we have
where 6, and 6, are determined by setting A = -3 and A = 2 in the equation
b0+b,A =An
Thus,
b,- 36, = (-3)"
b,+ 26, = 2"
from which we get
bO= $(-3)" + $(2)" 6, = - f(-3)"+ f(2)"
and
7.28. Using the spectral decomposition method, evaluate An for matrix A in Prob. 7.27.
Since the minimal polynomial of A is
which contains only simple factors, we can apply the spectral decomposition method to
evaluate A". Thus, by Eq. (7.33) we have
