# Documentation

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# Linear Model Identification Basics

Identified linear models, black-box modeling, model structure selection, and regularization

## Examples and How To

Identify Linear Models Using System Identification App

Identifying linear black-box models from single-input/single-output (SISO) data using the System Identification app.

Identify Linear Models Using the Command Line

Identifying linear models from multiple-input/single-output (MISO) data using System Identification Toolbox™ commands.

Transfer Function Structure Specification

Specify the values and constraints for the numerator, denominator and transport delays.

Specifying Initial Conditions for Iterative Estimation Algorithms

Specify how initial conditions are handled during model estimation in the app and at the command line.

Model Structure Selection: Determining Model Order and Input Delay

This example shows some methods for choosing and configuring the model structure.

Frequency Domain Identification: Estimating Models Using Frequency Domain Data

This example shows how to estimate models using frequency domain data.

Regularized Identification of Dynamic Systems

This example shows the benefits of regularization for identification of linear and nonlinear models.

Estimate Regularized ARX Model Using System Identification App

This example shows how to estimate regularized ARX models using automatically generated regularization constants in the System Identification app.

## Concepts

Types of Model Objects

Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.

System Identification Toolbox software uses objects to represent a variety of linear and nonlinear model structures.

Available Linear Models

A linear model is often sufficient to accurately describe the system dynamics and, in most cases, you should first try to fit linear models.

Linear Model Structures

Linear Model Structures

Black-Box Modeling

Black-box modeling is useful when your primary interest is in fitting the data regardless of a particular mathematical structure of the model.

Recommended Model Estimation Sequence

Recommended model estimation sequence, from the simplest to the more complex model structures.

Imposing Constraints on Model Parameter Values

All identified linear (IDLTI) models, except idfrd, contain a `Structure` property.

Determining Model Order and Delay

Estimation requires you to specify the model order and delay. Many times, these values are not known.

Effect of Input Intersample Behavior on Continuous-Time Models

The intersample behavior of the input signals influences the estimation, simulation and prediction of continuous-time models.

Modeling Multiple-Output Systems

Supported models for multiple-output systems.

Loss Function and Model Quality Metrics

Configure the loss function that is minimized during parameter estimation. After estimation, use model quality metrics to assess the quality of identified models.

Regularized Estimates of Model Parameters

Regularization is the technique for specifying constraints on the flexibility of a model, thereby reducing uncertainty in the estimated parameter values.

Estimation Report

The estimation report contains information about the results and options used for a model estimation.

Next Steps After Getting an Accurate Model

How you can work with identified models.