The following transfer functions show linear timeinvariant s

The following transfer functions show linear time-invariant systems. Write the dynamic equations (state equations and output equations) in vector-matrix form. (b) G(s) = 6/s^3 + 6s62 + 11s + 6 (c) G(s) = s + 2/s^2 + 7s + 12

Solution

(b)

>> n1=[6];
>> d1=[1 6 11 6];

>> [A1,B1,C1,D1] = TF2SS(n1,d1)

A1 =

    -6   -11    -6
     1     0     0
     0     1     0

B1 =

     1
     0
     0

C1 =

     0     0     6

D1 =

     0

(c)

>> n2=[1 2];
>> d2=[1 7 12];
>> [A2,B2,C2,D2] = TF2SS(n2,d2)

A2 =

    -7   -12
     1     0

B2 =

     1
     0

C2 =

     1     2

D2 =

     0