Page 407 - Schaum's Outline of Theory and Problems of Signals and Systems
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STATE SPACE ANALYSIS [CHAP. 7
Fig. 7-18
SOLUTIONS OF STATE EQUATIONS FOR DISCRETE-TIME LTI SYSTEMS
7.20. Find An for
by the Cayley-Hamilton theorem method.
First, we find the characteristic polynomial c(A) of A.
= - ?A + = (A - L)(A - L)
4 8 2 4
Thus, the eigenvalues of A are A, = i and A, = a. Hence, by Eqs. (7.27) and (7.28) we have
b1 I
An = b,I + b,A = i - b b,, + 36,
bo
and b, and b, are the solutions of
bo + b,(;) = (4)"
bo + b,(+) = ($)"
