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## 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. Available linear structures include transfer functions and state-space models, summarized in the following table.

Transfer function (`idtf`)

Use this structure to represent transfer functions:

`$y=\frac{num}{den}u+e$`

where num and den are polynomials of arbitrary lengths. You can specify initial guesses for, and estimate, num, den, and transport delays.

Transfer Function Models
Process model (`idproc`)Use this structure to represent process models that are low order transfer functions expressed in pole-zero form. They include integrator, delay, zero, and up to 3 poles. Process Models
State-space model (`idss`)Use this structure to represent known state-space structures and black-box structures. You can fix certain parameters to known values and estimate the remaining parameters. You can also prescribe minimum/maximum bounds on the values of the free parameters. If you need to specify parameter dependencies or parameterize the state-space matrices using your own parameters, use a grey-box model.State-Space Models
Polynomial models (`idpoly`)

Use to represent linear transfer functions based on the general form input-output polynomial form:

`$Ay=\frac{B}{F}u+\frac{C}{D}e$`

where A, B, C, D and F are polynomials with coefficients that the toolbox estimates from data.

Typically, you begin modeling using simpler forms of this generalized structure (such as ARX:$Ay=Bu+e$ and OE: $y=\frac{B}{F}u+e$) and, if necessary, increase the model complexity.

Input-Output Polynomial Models
Grey-box model (`idgrey`)Use to represent arbitrary parameterizations of state-space models. For example, you can use this structure to represent your ordinary differential or difference equation (ODE) and to define parameter dependencies.Linear Grey-Box Models

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