## Supported Continuous- and Discrete-Time Models

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 TypeDescription
Transfer function modelsEstimate 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 modelsTo 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 modelsEstimate 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) modelsIf 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) modelsIf 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 TypeDescription
Linear input-output polynomial modelsEstimate 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.

Nonlinear Model Identification

Estimate from time-domain data only.
Linear ODEs (grey-box) modelsIf 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) modelsIf the MATLAB file returns discrete-time output and state update values, estimate ordinary difference equations from time-domain data.

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