# Documentation

## Numeric Models

### Numeric Linear Time Invariant (LTI) Models

Numeric LTI models are the basic numeric representation of linear systems or components of linear systems. Use numeric LTI models for modeling dynamic components, such as transfer functions or state-space models, whose coefficients are fixed, numeric values. You can use numeric LTI models for linear analysis or control design tasks.

The following table summarizes the available types of numeric LTI models.

Model TypeDescription
`tf`Transfer function model in polynomial form
`zpk`Transfer function model in zero-pole-gain (factorized) form
`ss`State-space model
`frd`Frequency response data model
`pid`Parallel-form PID controller
`pidstd`Standard-form PID controller

### Identified LTI Models

Identified LTI Models represent linear systems with coefficients that are identified using measured input/output data. You can specify initial values and constraints for the estimation of the coefficients.

The following table summarizes the available types of identified LTI models.

Model TypeDescription
`idtf`Transfer function model in polynomial form, with identifiable parameters
`idss`State-space model, with identifiable parameters
`idpoly`Polynomial input-output model, with identifiable parameters
`idproc`Continuous-time process model, with identifiable parameters
`idfrd`Frequency-response model, with identifiable parameters
`idgrey`Linear ODE (grey-box) model, with identifiable parameters

### Identified Nonlinear Models

Identified Nonlinear Models represent nonlinear systems with coefficients that are identified using measured input/output data. You can specify initial values and constraints for the estimation of the coefficients.

The following table summarizes the available types of identified nonlinear models.

Model TypeDescription
`idnlarx`Nonlinear ARX model, with identifiable parameters
`idnlgrey`Nonlinear ODE (grey-box) model, with identifiable parameters
`idnlhw`Hammerstein-Wiener model, with identifiable parameters

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