For linear and nonlinear ODEs (grey-box models), you can specify any ordinary differential or difference equation to represent your continuous-time or discrete-time model in state-space form, respectively. In the linear case, both time-domain and frequency-domain data are supported. In the nonlinear case, only time-domain data is supported.

For black-box models, the following tables summarize supported continuous-time and discrete-time models.

**Supported Continuous-Time Models**

Model Type | Description |
---|---|

Transfer function models | Estimate continuous-time transfer function models directly
using `tfest` from either time-
and frequency-domain data.If you estimated a discrete-time transfer function model from time-domain data, then use `d2c` to transform it into a continuous-time
model. |

Low-order transfer functions (process models) | Estimate low-order process models for up to three free poles from either time- or frequency-domain data. |

Linear input-output polynomial models | To get a linear, continuous-time model of arbitrary structure
from time-domain data, you can estimate a discrete-time model, and
then use `d2c` to transform it
into a continuous-time model.You can estimate only polynomial models of Output Error structure using continuous-time frequency domain data.. Other structures that include noise models, such as Box-Jenkins (BJ) and ARMAX, are not supported for frequency-domain data. |

State-space models | Estimate continuous-time state-space models directly using
the estimation commands from either time- and frequency-domain data. If you estimated a discrete-time state-space model from time-domain data, then use `d2c` to
transform it into a continuous-time model. |

Linear ODEs (grey-box) models | If the MATLAB^{®} file returns continuous-time model matrices,
then estimate the ordinary differential equation (ODE) coefficients
using either time- or frequency-domain data. |

Nonlinear ODEs (grey-box) models | If the MATLAB file returns continuous-time output and state derivative values, estimate arbitrary differential equations (ODEs) from time-domain data. |

**Supported Discrete-Time Models**

Model Type | Description |
---|---|

Linear input-output polynomial models | Estimate arbitrary-order, linear parametric models from time-
or frequency-domain data. To get a discrete-time model, your data sample time must be set to the (nonzero) value you used to sample in your experiment. |

Estimate from time-domain data only. | |

Linear ODEs (grey-box) models | If the MATLAB file returns discrete-time model matrices, then estimate ordinary difference equation coefficients from time-domain or discrete-time frequency-domain data. |

Nonlinear ODEs (grey-box) models | If the MATLAB file returns discrete-time output and state update values, estimate ordinary difference equations from time-domain data. |

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