ss2tf and tf2ss function

Dear sir, I use ss2tf function in matlab. Its output values input to tf2ss function. But the result is not equal to the original input. (A1,B1,C1,D1) IS NOT EQUAL TO (A,B,C,D.)

What wrong is it?

clear;

A=[0 1 0;0 0 1;-9 -8 -7];

B=[7;8;9];

C=[2 3 4];

D=[0];

[num, den]=ss2tf(A,B,C,D,1);

[a1,b1,c1,d1]=tf2ss(num,den);

a1 =

   -7.0000   -8.0000   -9.0000
    1.0000         0         0
         0    1.0000         0

b1 =

     1
     0
     0

c1 =

   74.0000 -199.0000 -235.0000

d1 =

     0

Answer 1

The tf2ss() returns A,B,C,D matrices in controller (or controllable) canonical form. There is also observable canonical form. Bottom line, the A, B, C, D returned by tf2ss() may not match your original state space matrix. See state space controls

Answer 2

Hi dear david

keep in mind that representation of a system in frequency domain is unique

but we can convert it to state space form in many many ways...

so representation in state space form is not uniqe...

best regards