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Initial condition response of state-space model
initial(sys,x0)
initial(sys,x0,Tfinal)
initial(sys,x0,t)
initial(sys1,sys2,...,sysN,x0)
initial(sys1,sys2,...,sysN,x0,Tfinal)
initial(sys1,sys2,...,sysN,x0,t)
[y,t,x] = initial(sys,x0)
[y,t,x] = initial(sys,x0,Tfinal)
[y,t,x] = initial(sys,x0,t)
initial(sys,x0) calculates the unforced response of a state-space (ss) model sys with an initial condition on the states specified by the vector x0:
$$\begin{array}{cc}\dot{x}=Ax,& x(0)={x}_{0}\\ y=Cx& \end{array}$$
This function is applicable to either continuous- or discrete-time models. When invoked without output arguments, initial plots the initial condition response on the screen.
initial(sys,x0,Tfinal) simulates the response from t = 0 to the final time t = Tfinal. Express Tfinal in the system time units, specified in the TimeUnit property of sys. For discrete-time systems with unspecified sampling time (Ts = -1), initial interprets Tfinal as the number of sampling periods to simulate.
initial(sys,x0,t) uses the user-supplied time vector t for simulation. Express t in the system time units, specified in the TimeUnit property of sys. For discrete-time models, t should be of the form 0:Ts:Tf, where Ts is the sample time. For continuous-time models, t should be of the form 0:dt:Tf, where dt becomes the sample time of a discrete approximation to the continuous system (see impulse).
To plot the initial condition responses of several LTI models on a single figure, use
initial(sys1,sys2,...,sysN,x0)
initial(sys1,sys2,...,sysN,x0,Tfinal)
initial(sys1,sys2,...,sysN,x0,t)
(see impulse for details).
When invoked with output arguments,
[y,t,x] = initial(sys,x0)
[y,t,x] = initial(sys,x0,Tfinal)
[y,t,x] = initial(sys,x0,t)
return the output response y, the time vector t used for simulation, and the state trajectories x. No plot is drawn on the screen. The array y has as many rows as time samples (length of t) and as many columns as outputs. Similarly, x has length(t) rows and as many columns as states.