# idssdata

State-space data for identified system

## Syntax

## Description

## Examples

### Obtain Identified State-Space Matrices

Obtain the identified state-space matrices for a model estimated from data.

Identify a model using data.

load icEngine.mat data = iddata(y,u,0.04); sys = n4sid(data,4,'InputDelay',2);

`data`

is an `iddata`

object representing data sampled at a sampling rate of 0.04 seconds.

`sys`

is an `idss`

model representing the identified system.

Obtain identified state-space matrices of `sys`

.

[A,B,C,D,K] = idssdata(sys);

### Obtain Initial State of Identified Model

Obtain the initial state associated with an identified model.

Identify a model using data.

load icEngine.mat data = iddata(y,u,0.04); sys = n4sid(data,4,'InputDelay',2);

`data`

is an `iddata`

object representing data sampled at a sampling rate of 0.04 seconds.

`sys`

is an `idss`

model representing the identified system.

Obtain the initial state associated with `sys`

.

[A,B,C,D,K,x0] = idssdata(sys);

`A`

, `B`

, `C`

, `D`

and `K`

represent the state-space matrices of the identified model `sys`

. `x0`

is the initial state identified for `sys`

.

### Obtain Uncertainty Data of State-Space Matrices of Identified Model

Obtain the uncertainty matrices of the state-space matrices of an identified model.

Identify a model using data.

load icEngine.mat data = iddata(y,u,0.04); sys = n4sid(data,4,'InputDelay',2);

`data`

is an `iddata`

object representing data sampled at a sampling rate of 0.04 seconds.

`sys`

is an `idss`

model representing the identified system.

Obtain the uncertainty matrices associated with the state-space matrices of `sys`

.

[A,B,C,D,K,x0,dA,dB,dC,dD,dx0] = idssdata(sys);

`dA`

, `dB`

, `dC`

, `dD`

and `dK`

represent the uncertainty associated with the state-space matrices of the identified model `sys`

. `dx0`

represents the uncertainty associated with the estimated initial state.

### Obtain State-Space Matrices for Multiple Identified Models

Obtain the state-space matrices for multiple models from an array of identified models.

Identify multiple models using data.

load icEngine.mat data = iddata(y,u,0.04); sys2 = n4sid(data,2,'InputDelay',2); sys3 = n4sid(data,3,'InputDelay',2); sys4 = n4sid(data,4,'InputDelay',2); sys = stack(1,sys2,sys3,sys4);

`data`

is an `iddata`

object representing data sampled at a sampling rate of 0.04 seconds.

`sys`

is an array of `idss`

models. The first entry of `sys`

is a second-order identified system. The second and third entries of `sys`

are third- and fourth-order identified systems, respectively.

Obtain the state-space matrices for the first and third entries of `sys`

.

[A,B,C,D,K,x0] = idssdata(sys,1); [A,B,C,D,K,x0] = idssdata(sys,3);

### Obtain State-Space Matrices for Identified Model as Cell Array

Obtain the state-space matrices of an array of identified models in cell arrays.

Identify multiple models using data.

load icEngine.mat data = iddata(y,u,0.04); sys3 = n4sid(data,3,'InputDelay',2); sys4 = n4sid(data,4,'InputDelay',2); sys = stack(1,sys3,sys4);

`data`

is an `iddata`

object representing data sampled at a sampling rate of 0.04 seconds.

`sys`

is an array of `idss`

models. The first entry of `sys`

is a third-order identified system and the second entry is a fourth-order identified system.

Obtain the state-space matrices of `sys`

in cell arrays.

`[A,B,C,D,K,x0] = idssdata(sys,'cell');`

`A`

, `B`

, `C`

, `D`

and `K`

are cell arrays containing the state-space matrices of the individual entries of the identified model array `sys`

. `x0`

is a cell array containing the estimated initial state of the individual entries of the identified model array `sys`

.

## Input Arguments

`sys`

— Identified linear model

`idss`

| `idtf`

| `idproc`

| `idpoly`

| `idgrey`

| model array

Identified linear model, specified as one of the following model objects.

If `sys`

is not an identified state-space model
(`idss`

or `idgrey`

), then it is
first converted to an `idss`

model. This conversion
results in a loss of the model uncertainty information.

`sys`

can be an array of identified models.

`j1,...,jN`

— Model array indices

integers

Model array indices, specified as integers. Specify up to
*N* indices, where *N* is the number
of models in `sys`

.

## Output Arguments

`A`

, `B`

, `C`

, `D`

, `K`

— State-space matrices

arrays | cell array

State-space matrices that represent `sys`

as:

$$\begin{array}{l}x[k+1]=Ax[k]+Bu[k]+Ke[k];x[0]=x0;\\ y[k]=Cx[k]+Du[k]+e[k];\end{array}$$

If `sys`

is an array of identified models and you do
not specify the `'cell'`

input option, then
`A`

, `B`

, `C`

,
`D`

, and `K`

are multi-dimensional
arrays. To access a state-space matrix, such as `A`

, for
the *i*th entry in `sys`

, use
`A(:,:,`

.*i*)

If `sys`

is an array of identified models and you
specify the `'cell'`

input option, then
`A`

, `B`

, `C`

,
`D`

, and `K`

are cell arrays with
one entry for each model in `sys`

.

`x0`

— Initial states

column vector | matrix | cell array

Initial states, returned as a column vector or array.

If `sys`

is an `idss`

or
`idgrey`

model, then `x0`

contains
the initial state values obtained during estimation. These values are stored
in the `Report.Parameters`

property of
`sys`

.

For other model types, `x0`

is zero.

If `sys`

is an array of identified models and you do
not specify the `'cell'`

input option, then
`x0`

contains one column for each entry in
`sys`

.

If `sys`

is an array of identified models and you
specify the `'cell'`

input option, then
`x0`

is a cell array with one entry for each model in
`sys`

.

`dA`

, `dB`

, `dC`

, `dD`

, `dK`

— Uncertainties associated with the state-space matrices

arrays | cell arrays

Uncertainties associated with the state-space matrices
`A`

, `B`

, `C`

,
`D`

, and `K`

. The uncertainty
matrices represent one standard deviation of uncertainty.

If `sys`

is an array of identified models, then
`dA`

, `dB`

,
`dC`

, `dD`

, and
`dK`

are multi-dimensional arrays. To access the
state-space matrix, say A, for the *k*-th entry of
`sys`

, use
`A(:,:,`

.*k*)

If `sys`

is an array of identified models and you do
not specify the `'cell'`

input option, then
`dA`

, `dB`

,
`dC`

, `dD`

, and
`dK`

are multi-dimensional arrays. To access a
state-space matrix, such as `dA`

, for the
*i*th entry in `sys`

, use
`dA(:,:,`

.*i*)

If `sys`

is an array of identified models and you
specify the `'cell'`

input option, then
`dA`

, `dB`

,
`dC`

, `dD`

, and
`dK`

are cell arrays with one entry for each model in
`sys`

.

`dx0`

— Uncertainties associated with the initial states

column vector | matrix | cell array

Uncertainty associated with the initial states, returned as a column
vector or array. `dx0`

represents one standard deviation
of uncertainty.

If `sys`

is an array of identified models and you do
not specify the `'cell'`

input option, then
`dx0`

contains one column for each entry in
`sys`

.

If `sys`

is an array of identified models and you
specify the `'cell'`

input option, then
`dx0`

is a cell array with one entry for each model
in `sys`

.

## Version History

**Introduced in R2012a**

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