MATLAB: Discrete state space find and plot

discretelinear systemsloopplotstatespace

A = [0 1 0 0 0; -0.4 -1.3 0 0 0; 0 0 2 0 0; 0 0 0 0 -0.4; 0 0 0 1 -1.3];
B = [0; 1; 0; 0; 0];
C = [0 0 0 0 1]; 
x0 = transpose([0 0 0 0 0]); % initial condition
u = 1(k) % unit step
Find and plot:
x(k + 1) = A*x(k) + B*u(k)
How do I do this without using ss() and lsim(), and instead by using a for loop for 100 time units?
Thanks

Best Answer

Well, the nice thing about discrete time system is you can solve the discrete time equation with a loop.
clc;
clear all;
close all;
A = [0 1 0 0 0; -0.4 -1.3 0 0 0; 0 0 2 0 0; 0 0 0 0 -0.4; 0 0 0 1 -1.3];
B = [0; 1; 0; 0; 0];
C = [0 0 0 0 1]; 
x0 = transpose([0 0 0 0 0]); % initial condition
u = 1; % unit step
x(:,1) = A*x0 + B.*u;
% x(k + 1) = A*x(k) + B*u(k)
for k = 2:100
    x(:,k) = A*x(:,k-1) + B*u;
end
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