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Prévia do material em texto

Problem 7.07PP
Show that the transfer function is not changed by a linear transformation of state.
Step-by-step solution
step 1 of 2
Assume the original system,
X = PX-\-Ou 
y = H X - \ - J u
a(s) = H(si-py'a+j
Assume a change of state X to Z using the non singular transformation T,
y = n ^ + j u
0 (s ) = H ( S l- F y 'o + J
Assume a change of state X to Z using the non singular transformation T, 
X = T Z
The new system matrices are,
A = T ^ F T 
B =
C = H T 
D = J
Step 2 of 2
The transfer function is,
0 ,(S ) = C {S l-A y 'B + D
= H T [S I -T - 'F T y ^ ’r ^ a + J
a,{s)= htIst t ^-t 'ftY't -'o+j 
= H { S I -F y ''a + J 
= a{s)
I = o{s) I .