Page 423 - Schaum's Outline of Theory and Problems of Signals and Systems

STATE SPACE ANALYSIS [CHAP. 7

and b, and b, are the solutions of

from which we get

Hence,

7.40. Repeat Prob. 7.39 using the diagonalization method.
Let x be an eigenvector of A associated with A. Then
[A1 - A]x = 0

For A =A, = -2 we have

The solutions of this system are given by x, = - 2x1. Thus, the eigenvectors associated with A,
are those vectors of the form
Xl =a[ -;I with a # 0

For A =A2= -3 we have

The solutions of this system are given by x, = -3x,. Thus, the eigenvectors associated with A,
are those vectors of the form

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

Then