Modal realization in Matlab

Hi

Given the following transfer matrix :

T =

From input 1 to output:
    s - 1
-------------
s^2 + 3 s + 2

From input 2 to output:
      1
--------------
s^2 + 7 s + 12

Continuous-time transfer function.

I need to determine the modal representation (A is diag.) The following instruction gives me the right answer:

csys = canon(T,'modal')

csys =

a = 
     x1  x2  x3  x4
 x1  -2   0   0   0
 x2   0  -1   0   0
 x3   0   0  -4   0
 x4   0   0   0  -3

b = 
         u1      u2
 x1  -5.657       0
 x2  -4.472       0
 x3       0  -5.657
 x4       0      -5

c = 
          x1       x2       x3       x4
 y1  -0.5303   0.4472   0.1768     -0.2

d = 
     u1  u2
 y1   0   0

Continuous-time state-space model.

How can I get to the same representation analytically ?

Thanks

Answer 1

[River Rock]

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