How to generate multiple state spaces from arrays in MATLAB

Question

I would like to ask how to create multiple state-spaces from arrays.

Input is:

A1toA100 (100xn double)
B1toB100 (100xp double)
C1toC100 (100xn double)
D1toD100 (100xp double)

Example:

A1toA10 =

   -0.5909
   -0.4178
   -0.3412
   -0.2954
   -0.2643
   -0.2412
   -0.2233
   -0.2089
   -0.1970
   -0.1869

>> B1toB10

B1toB10 =

   33.3333
   33.3333
   33.3333
   33.3333
   33.3333
   33.3333
   33.3333
   33.3333
   33.3333
   33.3333

>> C1toC10

C1toC10 =

     1
     1
     1
     1
     1
     1
     1
     1
     1
     1

>> D1toD10

D1toD10 =

     0
     0
     0
     0
     0
     0
     0
     0
     0
     0

Where each of these contains a hundred of matrices of respective type (A,B,C or D).

Output should be:

SS1toSS100 (100x ss)

Where there would be a state space corresponding to each set of matrices.

Example for the first system:

With this code

ss([-0.5909],[33.3333],[1],[0])

I get a correct output. Four numbers, one system <1x1 ss>. This:

ans =

  a = 
            x1
   x1  -0.5909

  b = 
          u1
   x1  33.33

  c = 
       x1
   y1   1

  d = 
       u1
   y1   0

However with this code:

for i=1:2
    pom=[-0.5909 33.3333 1 0]
    SS1toSS10(i)=ss(pom(1),pom(2),pom(3),pom(4));
end

Although I should get 2 systems identical to the first one, I get this instead:

 SS1toSS10

SS1toSS10 =

  a = 
            x1       x2
   x1  -0.5909        0
   x2        0  -0.5909

  b = 
          u1     u2
   x1  33.33      0
   x2      0  33.33

  c = 
       x1  x2
   y1   1   1

  d = 
       u1  u2
   y1   0   0

Continuous-time state-space model.

Which is a wrong answer.

Approach 1:

for i=1:length(A1toA100)
    SS1toSS100(i)=ss(A1toA100(i),B1toB100,C1toC100,D1toD100);
end

This has generated 100 state spaces with matrix dimensions of 200x200, which is wrong, as I would expect dimensions of 2x2. Obviously the dimensions of entire matrices are considered.

Example output for Example input vectors:

S1toS10(1,1).a

-0,417825056426464  0   0   0   0   0   0   0   0   0
0   -0,341152729998142  0   0   0   0   0   0   0   0
0   0   -0,295446930748805  0   0   0   0   0   0   0
0   0   0   -0,264255768359200  0   0   0   0   0   0
0   0   0   0   -0,241231408801990  0   0   0   0   0
0   0   0   0   0   -0,223336886965331  0   0   0   0
0   0   0   0   0   0   -0,208912528213232  0   0   0
0   0   0   0   0   0   0   -0,196964620499203  0   0
0   0   0   0   0   0   0   0   -0,186857045774452  0
0   0   0   0   0   0   0   0   0   -0,590893861497609

S1toS10(1,1).b

0
0
0
0
0
0
0
0
0
33,3333333333333

S1toS10(1,1).c

1   1   1   1   1   1   1   1   1   1

S1toS10(1,1).d

0

Approach 2:

for i=1:length(A1toA100)
    SS1toSS100(i)=arrayfun(@ss,A1toA100(i),B1toB100,C1toC100,D1toD100);
end

Ends up with this error.

Error using arrayfun ss output type is not currently implemented.

Thank you for your help, Petr

Answer 1

Now I get your problem! Your last edit was essential.

The only way to store multiple state space models in one variable is a struct. Therefore your loop has to look like:

SS1toSS100(100) = struct;   %pre-allocation
for ii=1:100
    temp_ss = ss( A1toA100(ii) , B1toB100(ii) , C1toC100(ii) , D1toD100(ii) );
    SS1toSS100(ii) = struct('ss',temp_ss);
end

or even shorter:

SS1toSS100(100) = struct;   %pre-allocation
for ii=1:100
    SS1toSS100(ii).ss = ss( A1toA100(ii) , B1toB100(ii) , C1toC100(ii) , D1toD100(ii) );
end

which gives you a struct with 100 ss objects.

If you now want to access the 5th one for example, type:

SS1toSS100(5).ss

and you get

ans =

  a = 
            x1
   x1  -0.5909

  b = 
          u1
   x1  33.33

  c = 
       x1
   y1   1

  d = 
       u1
   y1   0

Continuous-time state-space model.

PS: don't use i as iteration variable it's a internal Matlab variable and reserved for complex numbers