State-space models are models that use state variables to describe a system by a set of first-order differential or difference equations, rather than by one or more nth-order differential or difference equations. State variables x(t) can be reconstructed from the measured input-output data, but are not themselves measured during an experiment.
The state-space model structure is a good choice for quick estimation because it requires you to specify only one input, the model order, n. The model order is an integer equal to the dimension of x(t) and relates to, but is not necessarily equal to, the number of delayed inputs and outputs used in the corresponding linear difference equation.
It is often easier to define a parameterized state-space model in continuous time because physical laws are most often described in terms of differential equations. In continuous-time, the state-space description has the following form:
The matrices F, G, H, and D contain elements with physical significance—for example, material constants. x0 specifies the initial states.
You can estimate continuous-time state-space model using both time-domain and frequency-domain data.
The discrete-time state-space model structure is often written in the innovations form that describes noise:
where T is the sample time, u(kT) is the input at time instant kT, and y(kT) is the output at time instant kT.
You cannot estimate a discrete-time state-space model using continuous-time frequency-domain data.
For more information, see What Are State-Space Models?
|System Identification||Identify models of dynamic systems from measured data|
|Estimate State-Space Model||Estimate state-space model using time or frequency data in the Live Editor|
|State-space model with identifiable parameters|
|Estimate state-space model using time-domain or frequency-domain data|
|Estimate state-space model by reduction of regularized ARX model|
|Estimate state-space model using subspace method with time-domain or frequency-domain data|
|Prediction error minimization for refining linear and nonlinear models|
State-space models are models that use state variables to describe a system by a set of first-order differential or difference equations, rather than by one or more nth-order differential or difference equations.
Choose between noniterative subspace methods, iterative method that uses prediction error minimization algorithm, and noniterative method.
To estimate a state-space model, you must provide a value of its order, which represents the number of states.
Modal, companion, observable and controllable canonical state-space models.
You can use time-domain and frequency-domain data that is real or complex and has single or multiple outputs.
Import data into the System Identification app.
Perform black-box or structured estimation.
Canonical parameterization represents a state-space system in a reduced parameter form where many elements of A, B and C matrices are fixed to zeros and ones.
This example shows how to estimate ARMAX and OE-form models using the state-space estimation approach.
The default parameterization of the state-space matrices A, B, C, D, and K is free; that is, any elements in the matrices are adjustable by the estimation routines.
Reduce the order of a Simulink® model by linearizing the model and estimating a lower-order model that retains model dynamics.
Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values.
An identified linear model is used to simulate and predict system outputs for given input and noise signals.
System Identification Toolbox™ software supports the following parameterizations that indicate which parameters are estimated and which remain fixed at specific values:
When you estimate state-space models, you can specify how the algorithm treats initial states.