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}]e.x'(t)=a.x(t)+b.u(t), y(t)=c.x(t)
    StateSpaceModel[{a,b,Automatic,Automatic,e}]e.x'(t)=a.x(t)+b.u(t), y(t)=x(t)
  • In StateSpaceModel[sys] the following systems can be converted:
  • AffineStateSpaceModelapproximate Taylor conversion
    NonlinearStateSpaceModelapproximate Taylor conversion
    TransferFunctionModelexact 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:
  • SamplingPeriodAutomaticthe sampling period
    StateSpaceRealizationAutomaticthe canonical realization
    DescriptorStateSpaceAutomaticstandard or descriptor realization
    SystemsModelLabelsAutomaticthe 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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Introduced in 2010
(8.0)
| Updated in 2014
(10.0)