%%% Section 1.4 
%%% State-Space modeling

clear
close all

X = [0;1]; 
dt = 0.1; 
A = [1 dt; 0 1];
B = [dt.^2/2;dt];
m = 2;
%u = 
T = 10;

for i=1:(T/dt)
    X(:,i+1) = A*X(:,i);% + B*round(rand)./m
end

figure(1)
plot([0:dt:T],X)
legend('position','velocity')
xlabel('time [sec]')
ylabel('meters, m/s')
%ylim([-.1,1.1])

X = [0;1];
for i=1:(T/dt)
    X(:,i+1) = A*X(:,i) + B*round(rand)./m;
end

figure(2)
plot([0:dt:T],X)
legend('position','velocity')
xlabel('time [sec]')
ylabel('meters, m/s')