K = 10;
T = 0.1;
zeta = sqrt(2)/2;
G = tf(K,[T^2 2*zeta*T 1])
Td = 0.05;
Gd = c2d(G,Td,'zoh')
[numd,dend] = tfdata(Gd,'v');
y1 = 0;
y2 = 0;
u1 = 0;
u2 = 0;
N = 21;
yd = zeros(N,1);
td = zeros(N,1);
u = 1;
for i = 1:N
    % rekurzivna relacija:
    y = -dend(2)*y1 - dend(3)*y2 + numd(2)*u1 + numd(3)*u2;
    y2 = y1;
    y1 = y;
    u2 = u1;
    u1 = u;
    yd(i) = y;
    td(i) = (i-1)*Td;
end
[ystep,tstep] = step(G,td(N));
plot(tstep,ystep)
hold on
stairs(td,yd)
xlabel('t[s]')
ylabel('y')
legend('kontinuirani','diskretni')

------------------------------------------------

A_=[-2/3 -2/3;2/3 -1/3]    %str 84
B_=[1 0;0 -1]
C_=[0 1;2/3 -1/3;1/3 1/3]
D_=[0 0;0 0;0 0]
[num,den]=ss2tf(A_,B_,C_,D_, 2)
G=(num,den)

G1 = tf(num(1,:),den)
G2 = tf(num(2,:),den)
G3 = tf(num(3,:),den)
p = eig(A_)
rank(A_)

%upravljivost i osmotrivost sustava
U = [B_ A_*B_ A_*A_*B_ A_*A_*A_*B_]
rank(U)
 O =[C_; C_*A_; C_*A_*A_; C_*A_*A_*A_]
rank(O)

%frekvencije
w_p1 = abs(imag(p(1)))
w_p2 = abs(imag(p(2)))
w_p3 = abs(imag(p(3)))
w_p4 = abs(imag(p(4)))
%periodi prigušenih i neprigušenih oscilacija
T_p1 = 2*pi/w_p1
T_p2 = 2*pi/w_p2
T_p3 = 2*pi/w_p3
T_p4 = 2*pi/w_p4