# Wolfram Language & System 10.0 (2014)|Legacy Documentation

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

# AffineStateSpaceModel

AffineStateSpaceModel[{a,b,c,d},x]
represents the affine state-space model , .

gives an affine state-space model corresponding to the system model sys.

AffineStateSpaceModel[eqns,{{x1,x10},}{{u1,u10},},{g1,},t]
gives the affine state-space model obtained by Taylor input linearization about the dependent variable at and input at of the differential equations eqns with outputs and independent variable t.

## Details and OptionsDetails and Options

• AffineStateSpaceModel is also known as an input linear model.
• AffineStateSpaceModel can represent any system where the control input occurs affinely, but still allows for advanced analysis and control design.
• The following short input forms can be used:
•  AffineStateSpaceModel[{a,b,c},x] output given by AffineStateSpaceModel[{a,b},x] output given by
• AffineStateSpaceModel[{a,b,},x,u,y,t] explicitly specifies the input variables u, output variables y, and independent variable t.
• AffineStateSpaceModel allows for operating values for the states x and inputs u.
• AffineStateSpaceModel[,{{x1,x10},},{{u1,u10},},] is used to indicate the operating values for the system. »
• In the following systems can be converted:
•  NonlinearStateSpaceModel approximate Taylor conversion StateSpaceModel exact conversion TransferFunctionModel exact conversion
• A system of ODEs with state equations and output equations is linearized at .
• The input-linearized system has state , input , and output , with state equations and output equation . The coefficient functions are given by , , , and , all evaluated at .
• A system of DAEs with state equations and output equations is linearized at .
• The input-linearized system has state , input , and output , with state equations and output equation . The coefficient functions are given by , , , , and , all evaluated at and .
• Differential equations that include higher-order derivatives of states and inputs are reduced to the cases above by introducing additional states.
• In computations where the operating points and are Automatic, it is assumed to be zero in functions such as OutputResponse and conversion to StateSpaceModel, or generic in functions such as ControllableModelQ.
• The following option can be given:
• AffineStateSpaceModel can be used in functions such as OutputResponse and SystemsModelSeriesConnect.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

The affine system with output :

 Out[1]=

Using equation-form input:

 Out[2]=

Its response to a unit-step input:

 Out[3]=