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Problem 7.09PP
Suppose we are given a system with state matrices A. B, C (D = 0 in this case). Find the 
transformation T so that, under Eqs. (1) and (2), the new state description matrices will be in 
observer canonical form.
Eqs. (1) 
A - T “ 'AT,
Eqs. (2)
C -c r . fi-D .
Step-by-step solution 
Step-by-step solution
step 1 of 4
(a)
Write the observer canonical form of the state space equations.
...... (1)
Write the output equation.
y - C . * , ...... (2)
Write the state description matrices in observer canonical form.
(3)
1 0 0
-Oi 0 1 0 0
A .= 0 0 0
0 0 0 1
0 0
c .= 1 0 0 0] (4)
D.= ..... (5)
Refer equation 7.21 in the textbook and write the equation for ^ matrix.
A = T - 'A T ...... (6)
Where,
X is transformation matrix.
Step 2 of 4
Write the general equation for transformation matrix.
T = [t, t ,] (7)
Modify equation (6).
; ^ = ATT-i
TA = A T .....