Hi @Hein zaw
In MATLAB, you can use the ODE solver approach. If the system is LTI and you have the Control System Toolbox installed, you can also use the lsim() command. However, I generally advise students to learn the ODE solver approach because it provides a more versatile skill that can be applied to both linear and nonlinear state-space systems, avoiding the need to learn something new when dealing with the latter.
% Call ode45 solver
tspan = linspace(0, 10, 1001);
x0 = [0, 0];
[t, x] = ode45(@odefcn, tspan, x0);
% Pre-allocate for the system output signal y
y = zeros(1, numel(t));
% Use for-loop to call odefcn() and compute y
for i = 1:numel(t)
[~, y(i)] = odefcn(t(i), x(i,:).');
end
figure
plot(t, x, 'linewidth', 1.5), hold on
plot(t, y, 'linewidth', 1.5), hold off, grid on
xlabel('Time'), legend('x_1', 'x_2', 'y', 'location', 'best')
% Create a function that returns two outputs (math): dxdt and y
function [dxdt, y] = odefcn(t, x)
% Inputs
u1 = heaviside(t);
u2 = 0.1*sin(2*pi/10*t);
u = [u1;
u2];
% Matrix definitions
A = [ 0 1; % state matrix
-2 -3];
B = [ 0 0; % input matrix
1 1];
C = [ 3 1]; % output matrix
D = 0*C*B; % direct matrix
% State-space system
dxdt = A*x + B*u; % state equation
y = C*x + D*u; % output equation (system)
end
