Page 408 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 71 STATE SPACE ANALYSIS

from which we get

bo = - (;ln + 2(;ln b, = 4($ - 4($)"

Hence,

7.21. Repeat Prob. 7.20 using the diagonalization method.

Let x be an eigenvector of A associated with A. Then
[Al - A]x = 0

For A=Al = ; we have

The solutions of this system are given by x, = 2x2. Thus, the eigenvectors associated with A,
are those vectors of the form

For A = A2 = $ we have

The solutions of this system are given by x, = 4x2. Thus, the eigenvectors associated with A,
are those vectors of the form

8+0

Let a = p = 1 in the above expressions and let

Then