For this example, generate a random state-space model with 5 states and create the plot for the system response to the initial states.

rng("default")
sys = rss(5);
x0 = [1,2,3,4,5];
initial(sys,x0)

Plot the response of the following state-space model:

Take the following initial condition:

a = [-0.5572, -0.7814; 0.7814, 0];
c = [1.9691  6.4493];
x0 = [1 ; 0];

sys = ss(a,[],c,[]);
initial(sys,x0)

Consider the following two-input, two-output dynamic system.

Convert the sys to state-space form since initial condition response plots are supported only for state-space models.

sys = ss([0, tf([3 0],[1 1 10]) ; tf([1 1],[1 5]), tf(2,[1 6])]);
size(sys)

State-space model with 2 outputs, 2 inputs, and 4 states.

The resultant state-space model has four states. Hence, provide an initial condition vector with four elements.

x0 = [0.3,0.25,1,4];

Create the initial condition response plot.

initial(sys,x0);

The resultant plot contains two subplots - one for each output in sys.

For this example, examine the initial condition response of the following zero-pole-gain model and limit the plot to tFinal = 15 s.

First, convert the zpk model to an ss model since initial only supports state-space models.

sys = ss(zpk(-1,[-0.2+3j,-0.2-3j],1)*tf([1 1],[1 0.05]));
tFinal = 15;
x0 = [4,2,3];

Now, create the initial conditions response plot.

initial(sys,x0,tFinal);

For this example, plot the initial condition responses of three dynamic systems.

First, create the three models and provide the initial conditions. All the models should have the same number of states.

rng('default');
sys1 = rss(4); 
sys2 = rss(4);
sys3 = rss(4);
x0 = [1,1,1,1];

Plot the initial condition responses of the three models using time vector t that spans 5 seconds.

t = 0:0.1:5;
initial(sys1,'r--',sys2,'b',sys3,'g-.',x0,t)

Extract the initial condition response data of the following state-space model with two states:

Use the following initial conditions:

a = [-0.5572, -0.7814; 0.7814, 0];
c = [1.9691  6.4493];
x0 = [1 ; 0];
sys = ss(a,[],c,[]);
[y,tOut,x] = initial(sys,x0);

The array y has as many rows as time samples (length of tOut) and as many columns as outputs. Similarly, x has rows equal to the number of time samples (length of tOut) and as many columns as states.

For this example, extract the initial condition response data of a state-space model with 6 states, 3 outputs and 2 inputs.

First, create the model and provide the initial conditions.

rng('default');
sys = rss(6,3,2); 
x0 = [0.1,0.3,0.05,0.4,0.75,1];

Extract the initial condition responses of the model using time vector t that spans 15 seconds.

t = 0:0.1:15;
[y,tOut,x] = initial(sys,x0,t);

The array y has as many rows as time samples (length of tOut) and as many columns as outputs. Similarly, x has rows equal to the number of time samples (length of tOut) and as many columns as states.