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State-Space Models

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


System IdentificationIdentify models of dynamic systems from measured data

Live Editor Tasks

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


ssestEstimate state-space model using time-domain or frequency-domain data
ssregestEstimate state-space model by reduction of regularized ARX model
n4sidEstimate state-space model using subspace method with time-domain or frequency-domain data
idssState-space model with identifiable parameters
pemPrediction error estimate for linear and nonlinear model
delayestEstimate time delay (dead time) from data
getpvecModel parameters and associated uncertainty data
setpvecModify value of model parameters
getparObtain attributes such as values and bounds of linear model parameters
setparSet attributes such as values and bounds of linear model parameters
ssformQuick configuration of state-space model structure
initSet or randomize initial parameter values
idparCreate parameter for initial states and input level estimation
idssdataState-space data of identified system
findstatesEstimate initial states of model
ssestOptionsOption set for ssest
ssregestOptionsOption set for ssregest
n4sidOptionsOption set for n4sid
findstatesOptionsOption 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.


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.