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

System Identification | Identify models of dynamic systems from measured data |

`ssest` |
Estimate state-space model using time or frequency domain data |

`ssregest` |
Estimate state-space model by reduction of regularized ARX model |

`n4sid` |
Estimate state-space model using subspace method |

`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 |

**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.

*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 *n*th-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:

**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.

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