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 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.
Nonlinear Model Identification	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.