FOR LOOP with constant matrix

Dear All,

I want to create FOR LOOP by Matlab to solve this equation :

x(t+dt)=(dt*A+I)*x(t)+B*dt

in which

A =[0 1;-6 -5]
I=eye(2)
B=[0;1]
dt=0.01

initial condition

x(0)=[0;0]
x(t) = vector 2x1

Any one can give me some ideas ?

I have created some scripts in m file as per below :

ft=1;            % Step Input
dt=0.01;        % Time Interval (can be changed)    
t_end=5;         % End of Time for plotting (fix)
Nstep=round(t_end/dt);
Xo=zeros(2,1);       % Initial Condition for X, at t=0
Xdot0=A*Xo+B*ft; % Intitial Condition for Xdot, at t=0
Y=C*Xdot0;       % Intitial Condition for Y, at t=0
I=eye(size(A));  % Identity Matrix
for i=1:Nstep
    x(i)= Xo
    x(i+1)=(dt*A+I)*x(i)+B*dt;
end

However, It does not work

Thanks a lot Wildany

Answer 1

[Jan]

Avoid "it does not work" in question. Better explain any details, e.g. if you get an error message (then add a complete copy) or if the results differ from your expectations (then describe both).

x is an array and in consequence x(i) is a scalar. You cannot assign the vector Xo to a scalar element of a vector.

If i is increased by 1 in each iteration, you overwrite the former value in x(i+1) .

ft    = 1;       % Step Input
dt    = 0.01;    % Time Interval (can be changed)    
t_end = 5;       % End of Time for plotting (fix)
Nstep = round(t_end / dt);
X     = zeros(2, Nstep);  % Pre-allocate the complete solution
X(:, 1) = [0;0]; % Initial Condition for X, at t=0

% Not used, so omit it:
% Xdot0=A*Xo+B*ft; % Intitial Condition for Xdot, at t=0
% Y=C*Xdot0;       % Intitial Condition for Y, at t=0

I = eye(size(A));  % Identity Matrix
B = [0;1];         % Was missing ?

for i = 2:Nstep    % 1st step defined already
    x(:, i) = (dt*A+I) * x(:, i-1) + B*dt;
end