ssArray = sample(vSys,T)
samples the dynamics of the linear time-varying (LTV) model vSys at
the times specified in the time vector T and returns an array of
time-invariant state-space (ss) models.

ssArray = sample(vSys,T,P)
samples the dynamics of the linear-parameter varying (LPV) model vSys
at the single point (T,P) and returns an array
of time-invariant state-space (ss) models. Set T to
[] if the dynamics of the LPV model only depend on
P.

ssArray = sample(vSys,T,P1,...,Pn)
samples the dynamics over a grid of (T,P)
values. P1,...,Pn are arrays specifying the values of each parameter of
the LPV model.

ssArray = sample(vSys,S)
specifies the sample values as a structure S.

ssArray = sample(vSys)
samples a gridded LTV or LPV model at values obtained from vSys.Grid.
You can use this syntax as a quick way to access the state-space data and offsets used to
construct the gridded LTV or LPV model.

[ssArray,offsets] = sample(___)
also returns a structure array offsets containing the derivative,
state, input, and output offset values at the specified times. You can use this syntax
with any of the input-argument combinations in previous syntaxes.

You can sample the dynamics of an LTV model over a point or a vector
of $\mathit{t}$ values to obtain affine dynamics for a given time.

Consider a model defined by the data function
ltvssDataFcn.m.

Create an LTV model.

ltvSys = ltvss(@ltvssDataFcn)

Continuous-time state-space LTV model with 1 outputs, 1 inputs, and 1 states.
Model Properties

Define a set of times values to sample this model over.

t = 5:0.5:10;

Use the psample command to obtain an array of
ss models.

ssArray = psample(ltvSys,t);
size(ssArray)

1x11 array of state-space models.
Each model has 1 outputs, 1 inputs, and 1 states.

In ssArray, the SamplingGrid property tracks
the dependence of each model on time and the Offsets property
contains the offset values as a function of time.

ssArray.SamplingGrid

ans = struct with fields:
Time: [5 5.5000 6 6.5000 7 7.5000 8 8.5000 9 9.5000 10]

ssArray.Offsets

ans=1×11 struct array with fields:
dx
x
u
y

View the data function.

type ltvssDataFcn.m

function [A,B,C,D,E,dx0,x0,u0,y0,Delays] = ltvssDataFcn(t)
% SISO, first order
A = -(1+0.5*sin(t));
B = 1;
C = 1;
D = 0;
E = [];
dx0 = [];
x0 = [];
u0 = [];
y0 = 0.1*sin(5*t);
Delays = [];

vSys — Varying model to sample ltvss object | lpvss object

Varying model to sample, specified as an ltvss or
lpvss object.

T — Time values scalar | vector | array

Time values at which the model is sampled.

For LTV models, specify T as a scalar or vector for real
and finite values to sample the dynamics at a single time value or multiple ones,
respectively.

For LPV models, specify T as one of the following:

[] — LPV model dynamics only depend only on parameters
p.

Scalar — Sample the dynamics at a single time value.

Vector — Sample the dynamics at multiple time values.

Multidimensional array — Sample the dynamics at a grid of values. You must
specify a rectangular (T,P) grid of
values, such as the ones you create using ndgrid.

[t,p1,p2,p3] = ndgrid(tvals,p1vals,p2vals,p3vals)

The vectors or arrays T and P1,...,Pn
must be of the same size.

In discrete time, specify T as integer index values
k that count the number of sampling periods Ts.
The absolute time is given by t = k*Ts.

P — Parameter values scalar | vector | array

Parameter values at which the LPV model is sampled.

For an LPV model with n parameters, use comma-separated arguments
P1,...,Pn to specify the values for each parameter.

Specify P as one of the following:

Scalar — Sample the dynamics at a single parameter value.

Vector — Sample the dynamics at multiple parameter values.

Multidimensional array — Sample the dynamics at a grid of values. You must
specify a rectangular (T,P) grid of
values, such as the ones you create using ndgrid.

[t,p1,p2,p3] = ndgrid(tvals,p1vals,p2vals,p3vals)

The vectors or arrays T and P1,...,Pn
must be of the same size.

S — Sampling grid structure struct

Sampling grid structure array used to specify values at which the model is
sampled.

For LTV models, S is a structure array with field
Time. For example, if an array Tvalues
specifies the sampling time, S is the following
structure.

S = struct('Time',Tvalues)

For LPV models, S is a structure with fields for parameter
names corresponding to the ParameterName property of the
lpvss model vSys and
Time. For example, if vSys has two
parameters named 'speed' and 'altitude' with
values specified using arrays P1vals and
P2vals, respectively, S is the following
structure.

S = struct('speed',P1vals,'altitude',P2vals)

If the dynamics of your LPV model depend on parameter values, do not specify the
field Time for S.

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