State-Space Models

State-space models with free, canonical, and structured parameterizations; equivalent ARMAX and OE models

Apps

Identify models of dynamic systems from measured data

Live Editor Tasks

Estimate state-space model using time or frequency data in the Live Editor

Functions

`ssest`	Estimate state-space model using time-domain or frequency-domain data
`ssregest`	Estimate state-space model by reduction of regularized ARX model
`n4sid`	Estimate state-space model using subspace method with time-domain or frequency-domain data
`idss`	State-space model with identifiable parameters
`pem`	Prediction error estimate for linear and nonlinear model

`delayest`	Estimate time delay (dead time) from data
`getpvec`	Model parameters and associated uncertainty data
`setpvec`	Modify value of model parameters
`getpar`	Obtain attributes such as values and bounds of linear model parameters
`setpar`	Set attributes such as values and bounds of linear model parameters
`ssform`	Quick configuration of state-space model structure
`init`	Set or randomize initial parameter values
`idpar`	Create parameter for initial states and input level estimation
`idssdata`	State-space data of identified system
`findstates`	Estimate initial states of model

`ssestOptions`	Option set for `ssest`
`ssregestOptions`	Option set for `ssregest`
`n4sidOptions`	Option set for `n4sid`
`findstatesOptions`	Option set for `findstates`

Examples and How To

Estimate State-Space Model With Order Selection

To estimate a state-space model, you must provide a value of its order, which represents the number of states.

Estimate State-Space Models in System Identification App

Import data into the System Identification app.

Estimate State-Space Models at the Command Line

Perform black-box or structured estimation.

Estimate State-Space Models with Free-Parameterization

The default parameterization of the state-space matrices A, B, C, D, and K is free; that is, any elements in the matrices are adjustable by the estimation routines.

Estimate State-Space Models with Canonical Parameterization

Canonical parameterization represents a state-space system in a reduced parameter form where many elements of A, B and C matrices are fixed to zeros and ones.

Estimate State-Space Models with Structured Parameterization

Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values.

Estimate State-Space Equivalent of ARMAX and OE Models

This example shows how to estimate ARMAX and OE-form models using the state-space estimation approach.

Use State-Space Estimation to Reduce Model Order

Reduce the order of a Simulink^® model by linearizing the model and estimating a lower-order model that retains model dynamics.

Concepts

What Are State-Space Models?

State-space models are models that use state variables to describe a system by a set of first-order differential or difference equations, rather than by one or more nth-order differential or difference equations.

Data Supported by State-Space Models

You can use time-domain and frequency-domain data that is real or complex and has single or multiple outputs.

Supported State-Space Parameterizations

System Identification Toolbox™ software supports the following parameterizations that indicate which parameters are estimated and which remain fixed at specific values:

Canonical State-Space Realizations

Modal, companion, observable and controllable canonical state-space models.

Specifying Initial States for Iterative Estimation Algorithms

When you estimate state-space models, you can specify how the algorithm treats initial states.

State-Space Model Estimation Methods

Choose between noniterative subspace methods, iterative method that uses prediction error minimization algorithm, and noniterative method.

Identifying State-Space Models with Separate Process and Measurement Noise Descriptions

An identified linear model is used to simulate and predict system outputs for given input and noise signals.

System Identification Toolbox Documentation

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