How to plot y = C*expm(A*t)*B?

How to plot y = C*expm(A*t)*B, where A,B and C are matrices? I tried defining t=linspace(0,100,25) and then calculate y as function (as defined) and I got message about dimension error.

Answer 1

[Star Strider]

This works:

A = [1 -4; 3 -5];                                   % Define System Matrices
B = [1; 1];
C = [1 0; 0 1];

N = 50;                                             % Length Of Simulation (Samples)
t = linspace(0, 5, N);                              % Time Vector
u = ones(2, N);                                     % System Input
for k1 = 1:length(t);
    y(:,k1) = C*expm(A*t(k1))*B.*u(:,k1);           % Evaluate System At Each Time & Input
end

figure(1)
plot(t, y)
grid

[Ljix]

Thank you.Can you please explain the dot next to B? Why is that?

[Star Strider]

The dot is an operator that converts the matrix multiplication operator (*) to an element-wise operator (.*). See the documentation for Array vs. Matrix Operations for a fun and interesting time!

[Star Strider]

The (1x2) vector for ‘C’ should work, because the other matrices are (2x2). It would then produce a column-vector output.

The problem is with ‘u=ones(1,N)’. The ‘u’ vector has to have two rows at any time (or equivalently, index) to work in my example, although they do not have to be all 1. The ‘u’ is the input to the dynamical system, so it can have any value, providing that every column presented to the system as an input has two rows. That is likely where the dimension error originates.