# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# StateSpaceModel

StateSpaceModel[{a,b,c,d}]
represents the standard state-space model with state matrix a, input matrix b, output matrix c, and transmission matrix d.

StateSpaceModel[{a,b,c,d,e}]
represents a descriptor state-space model with descriptor matrix e.

StateSpaceModel[sys]
gives a state-space model corresponding to the systems model sys.

StateSpaceModel[eqns,{{x1,x10},},{{u1,u10},},{g1,},τ]
gives the state-space model obtained by Taylor linearization about the point of the differential or difference equations eqns with outputs and independent variable τ.

## Details and OptionsDetails and Options

• StateSpaceModel can represent scalar and multivariate systems in continuous or discrete time.
• Time delays can be represented in any state-space model, by using SystemsModelDelay in any of the matrices.
• A continuous-time system modeled by the equations with states , control inputs , and outputs can be specified as StateSpaceModel[{a,b,c,d}].
• A discrete-time system modeled by the equations with states , control inputs , outputs , and sampling period τ can be specified as StateSpaceModel[{a,b,c,d},SamplingPeriod->τ].
• Continuous-time and discrete-time descriptor state-space systems can be specified as follows:
•  StateSpaceModel[{a,b,c,d,e}] StateSpaceModel[{a,b,c,d,e},SamplingPeriod->τ]
• For a system with n states, p inputs, and q outputs, the matrices a, b, c, d and e should have dimensions , , , , and .
• The following short inputs can be used:
•  StateSpaceModel[{a,b,c}] StateSpaceModel[{a,b}] StateSpaceModel[{a,b,c,Automatic,e}] StateSpaceModel[{a,b,Automatic,Automatic,e}]
• In StateSpaceModel[sys] the following systems can be converted:
•  AffineStateSpaceModel approximate Taylor conversion NonlinearStateSpaceModel approximate Taylor conversion TransferFunctionModel exact conversion
• When converting from transfer-function model sys, the controllable realization is used.
• For equational input, default linearization points and are taken to be zero.
• The following options can be given:
•  SamplingPeriod Automatic the sampling period StateSpaceRealization Automatic the canonical realization DescriptorStateSpace Automatic standard or descriptor realization SystemsModelLabels Automatic the labels for the input, output, and state variables

## ExamplesExamplesopen allclose all

### Basic Examples  (5)Basic Examples  (5)

A state-space model of an integrator:

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A secondorder single-input, single-output system:

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The state-space model of a transfer-function object:

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The state-space model of a system with sampling period τ:

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The state-space model of a set of ODEs:

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### Properties & Relations  (14)Properties & Relations  (14)

Introduced in 2010
(8.0)
| Updated in 2014
(10.0)