What to do in the case of a matrix 2x2 .......tf2ss

Convert it to state-space form using tf2ss.

b = [0 2 3; 1 2 1];

a = [1 0.4 1];

[A,B,C,D] = tf2ss(b,a)

A = 2×2

-0.4000 -1.0000

1.0000 0

B = 2×1

1

0

C = 2×2

2.0000 3.0000

1.6000 0

D = 2×1

0

1

Answer 1

[Star Strider]

Note that the present problem uses the Control System Toolbox. The tf2ss function is in the Signal Processing Toolbox. To convert Control System Toolbox models from transfer functions to state space, use ss instead.

The correct procedure to do what you want is:

s = tf('s');                                % Define Continuous Time
b = {[0 2 3]; [1 2 1]};                     % Numerator Cell Array
a = [1 0.4 1];                              % Denominator Vector (Cell Array If Different Denominators)
systf = tf(b,a)                             % Define Transfer Function
sysss = ss(systf)                           % Convert To State Space Representation

producing:

systf =
 
  From input to output...
           2 s + 3
   1:  ---------------
       s^2 + 0.4 s + 1
 
        s^2 + 2 s + 1
   2:  ---------------
       s^2 + 0.4 s + 1
 
Continuous-time transfer function.


sysss =
 
  A = 
         x1    x2
   x1  -0.4    -1
   x2     1     0
 
  B = 
       u1
   x1   2
   x2   0
 
  C = 
        x1   x2
   y1    1  1.5
   y2  0.8    0
 
  D = 
       u1
   y1   0
   y2   1
 
Continuous-time state-space model.

Remember that to simulate it, the input signal ‘u’ must be the same column size as ‘B’, for example:

[u,t] = gensig('square',4,10,0.1);
u = u*ones(1,size(sysss.B,2));              % Create Appropriate Size for ‘u’
lsim(sysss,u,t)

This will automatically adjust to give the same vector to each input of a MIMO or MISO system. If you want different vectors to different inputs, they need to be individually created.

Experiment to get different results.