Matlab ko zna koji

>> A = [1 1 ; 4 -2]

A =

     1     1
     4    -2

>> B = [1 -1; 1 -1]

B =

     1    -1
     1    -1

>> D = 0

D =

     0

>> Co = ctrb(A,B)

Co =

     1    -1     2    -2
     1    -1     2    -2

>> unicon_states = length(A) - rank(Co)

unicon_states =

     1

>> Ob = obav(A,B)
Undefined function or variable 'obav'.

Did you mean:
>> Ob = obsv(A,B)

Ob =

     1    -1
     1    -1
    -3     3
    -3     3

>> Ob = obav(A,C)
Undefined function or variable 'C'.

>> Ob = obav(A,Co)
Undefined function or variable 'obav'.

Did you mean:
>> Ob = obsv(A,Co)
Error using obsv (line 28)
In the "obsv(A,C)" command, the A matrix must be square with as many columns as C.

>> unicon_states = length(A) - rank(B)

unicon_states =

     1

>> unicon_states = length(A) - rank(Co)

unicon_states =

     1

>> Co = ctrb(A,B)

Co =

     1    -1     2    -2
     1    -1     2    -2

>> unicon_states = length(A) - rank(Co)

unicon_states =

     1

>> Ob = obav(A,Co)
Undefined function or variable 'obav'.

Did you mean:
>> Ob = obsv(A,Co)
Error using obsv (line 28)
In the "obsv(A,C)" command, the A matrix must be square with as many columns as C.

>> Ob = obsv(A,Co)
Error using obsv (line 28)
In the "obsv(A,C)" command, the A matrix must be square with as many columns as C.

>> Ob = obsv(A,B)

Ob =

     1    -1
     1    -1
    -3     3
    -3     3

>> neosmotrivaStanja = length(A) - rank(Ob)

neosmotrivaStanja =

     1

>> Gs = tf([1 0], 1)

Gs =

  s

Continuous-time transfer function.

>> num1 = [2,0]; den1 = [4,1];
>> num2 = [3]; den2=[5,1];
>> Gs1=tf(num1,den1);
>> Gs2=tf(num2,den2);
>> Gs = [Gs1, Gs2]

Gs =

  From input 1 to output:
    2 s
  -------
  4 s + 1

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

Continuous-time transfer function.

>> %prvi deo nije nesto tacan za Co
>> num = {[1 1]; 1}; den = {[1 2 2]; [1 0]};
>> Gs = tf(num,den)

Gs =

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

       1
   2:  -
       s

Continuous-time transfer function.

>> numd = [1 0.5]; dend = [1,1.5,2]; Tsd = 0.4;
>> Ob = obav(A,Co)
Undefined function or variable 'obav'.

Did you mean:
>> Ob = obsv(A,Co)
Error using obsv (line 28)
In the "obsv(A,C)" command, the A matrix must be square with as many columns as C.

>> Ob = obsv(A,Co)
Error using obsv (line 28)
In the "obsv(A,C)" command, the A matrix must be square with as many columns as C.

>> Gz = tf(numd, dend, Tsd)

Gz =

      z + 0.5
  ---------------
  z^2 + 1.5 z + 2

Sample time: 0.4 seconds
Discrete-time transfer function.

>> s = tf('s');
>> Gs = s/(s^2 + 2*s + 10);
>> Gs = tf([1 0], [1 2 10]);
>> F = [0,1; -4,-2];
>> G = [0;-2];
>> H = [1,0];
>> D = [0];
>> ss1 = ss(F,G,H,D)

ss1 =

  a =
       x1  x2
   x1   0   1
   x2  -4  -2

  b =
       u1
   x1   0
   x2  -2

  c =
       x1  x2
   y1   1   0

  d =
       u1
   y1   0

Continuous-time state-space model.

>> ss1.a

ans =

     0     1
    -4    -2

>> F = [-1 0; 0 -1];
>> G = [1;0];
>> H = eye(2);
>> D = zeros(2,1);
>> sys = ss(F,G,H,D,0.4)

sys =

  a =
       x1  x2
   x1  -1   0
   x2   0  -1

  b =
       u1
   x1   1
   x2   0

  c =
       x1  x2
   y1   1   0
   y2   0   1

  d =
       u1
   y1   0
   y2   0

Sample time: 0.4 seconds
Discrete-time state-space model.

>> %ss2tf, tf2ss, tf2zp, ss2zp, c2d, d2c, size [*broj izlaza i ulaza sistema]
>> sys = ss(F,G,H,D)

sys =

  a =
       x1  x2
   x1  -1   0
   x2   0  -1

  b =
       u1
   x1   1
   x2   0

  c =
       x1  x2
   y1   1   0
   y2   0   1

  d =
       u1
   y1   0
   y2   0

Continuous-time state-space model.

>> tf(sys)

ans =

  From input to output...
         1
   1:  -----
       s + 1

   2:  0

Continuous-time transfer function.

>> [num, den] = ss2tf(F,G,H,D,1) %poslednji argument broj izlaza

num =

     0     1     1
     0     0     0


den =

     1     2     1

>>
>> [num,den] = mason{'zadatak.net', 1, 7}
Undefined variable "mason" or class "mason".

>> [num,den] = mason('zadatak.net', 1, 7)
     1     1     2
     2     2     3
     3     3     4
     4     4     5
     5     5     6
     6     6     7
     7     2     4
     8     2     5
     9     6     5
    10     6     4
    11     6     3

    '(1)'    '(-3)'    '(1/z)'    '(1/z)'    '(1/z)'    '(1)'    '(2)'    '(1)'    '(-6)'    '(-12)'    '(-8)'


-- Network Info --
Net File   : zadatak.net
Start Node : 1
Stop Node  : 7

----- Paths -----
P1 : 1 2 3 4 5 6
P2 : 1 7 4 5 6
P3 : 1 8 5 6

- Order 1 Loops -
L11 : 3 4 5 11
L12 : 4 5 10
L13 : 5 9

The variables returned are strings describing
the numerator and Denominator of the transfer equation.
If you have the symbolic toolbox, use Denominator=sym(Denominator)
and Numerator=sym(Numerator) to make these symbolic equations.
You can now use simple(Numerator/Denominator) to boil the whole
thing down. You could also use simple(Numerator) to simplify the
Numerator on it' own.


num =

((((1)*(-3)*(1/z)*(1/z)*(1/z)*(1)*(1)-0)+(1)*(2)*(1/z)*(1/z)*(1)*(1)-0)+(1)*(1)*(1/z)*(1)*(1)-0)


den =

1-((1/z)*(1/z)*(1/z)*(-8)+(1/z)*(1/z)*(-12)+(1/z)*(-6))

>> num = sym(num)

num =

1/z + 2/z^2 - 3/z^3

>> den = sym(den)

den =

6/z + 12/z^2 + 8/z^3 + 1

>> Gz = simplify(num/den)

Gz =

(z^2 + 2*z - 3)/(z + 2)^3

>> %odrediti nule i polove ove prenosne funkcije i da se ispita upravljivost i osmotrivost ovog sistema
>> [num,den] = numden(Gz)

num =

z^2 + 2*z - 3


den =

(z + 2)^3

>> [F,G,H] = tf2ss(sym2poly(num), sym2poly(den))

F =

    -6   -12    -8
     1     0     0
     0     1     0


G =

     1
     0
     0


H =

     1     2    -3

>> C = ctrb(F,G)

C =

     1    -6    24
     0     1    -6
     0     0     1

>> upravljivost = length(F) - rank(C)

upravljivost =

     0

>> %jeste upravljiva jer ima nula neupravljivih stanja
>> O = obav(F,H)
Undefined function or variable 'obav'.

Did you mean:
>> O = obsv(F,H)

O =

     1     2    -3
    -4   -15    -8
     9    40    32

>> neosmotrivastanja = length(F) - rank(O)

neosmotrivastanja =

     0

>>