lsim

Simulates LTI model response to arbitrary inputs.

Syntax

[Y, T, X] = lsim(SYS, U)

[Y, T, X] = lsim(SYS, U, T)

[Y, T, X] = lsim(SYS, U, T, X0)

Inputs

SYS
A state-space or transfer function model. The model must have at least as many poles as zeros.
U
The signal vector.
T
The time vector.
X0
The state vector initial conditions. Default = a zero vector.

Outputs

Y
The output response matrix.
Note: The outputs are stored by column.
T
The time vector.
X
The state trajectories matrix.
Note: The trajectories are stored by column.

Example

Plot state trajectories:


Figure 1.
 A = [-20 -40 -60;1  0  0; 0  1  0];
B = [1;   0;   0];
C = [0   0   1];
D = 0;
T = [0:0.1:1];        % Time vector
U = zeros(size(T,1), size(T,2));    
X0 = [0.1 0.1 0.1];   % Initial Condition
sys = ss(A, B, C, D);    
[y, t, x] = lsim(sys, U, T, X0);
plot(t,x);
xlabel('Time (sec)');
ylabel('State Trajectory');
grid;