lsim
Plot simulated time response of dynamic system to arbitrary inputs.
📝Syntax
lsim(sys, u, t)
lsim(sys, u, t, x0)
[y, tOut, x] = lsim(SYS, U, T, X0)
📥Input Arguments
Parameter Description
sys a lti model.
u Input signal: matrix or vector.
t Time samples: vector.
x0 Initial state values: vector.
📤Output Arguments
Parameter Description
y Simulated response data: matrix or vector.
tOut Time vector: vector.
x State trajectories: matrix or vector.
📄Description

The functionlsim(sys, u, t) generates a plot illustrating the simulated time response of the dynamic system modelsys to the input history (t, u).

The time samples for the simulation are specified by the vectort.

In the case of single-input systems, the input signalu is a vector with the same length as t.

For multi-input systems,u is an array with rows corresponding to time samples (length(t)) and columns corresponding to inputs tosys.

An additional usage of the function is demonstrated by the examplelsim(sys, u, t, x0), where a vectorx0 is provided to specify initial state values.

This is particularly relevant whensys is a state-space model.

💡Examples
A = [-10 -20 -30;1  0  0; 0  1  0];
B = [1;   0;   0];
C = [0   0   1];
D = 0;
T = [0:0.1:1];
U = zeros(size(T, 1), size(T, 2));    
X0 = [0.1 0.1 0.1];
sys = ss(A, B, C, D);    
lsim(sys, U, T, X0);
Example illustration 
A = [-1.7  -0.3   1.1;
     -0.2  -1.7   0.6;
      1.0   0.6  -1.4];
B = [ 1.5  0.6;
     -1.8  1.0;
      0    0  ];
C = [ 0    -0.5 -0.1;
      0.35 -0.1 -0.15
      0.65  0    0.6];
D = [ 0.5  0;
      0.05 0.75
      0    0];
sys = ss(A,B,C,D);
Tf = 10;
Ts = 0.1;
[uSq,t] = gensig("square",4,Tf,Ts);
uP = gensig("pulse",3,Tf,Ts);
u = [uSq uP];
lsim(sys,u,t)
Example illustration
🔗See Also
gensigstep
🕔Version History
Version Description
1.0.0 initial version
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