# 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 (xi0,ui0) of the differential or difference equations eqns with outputs gi and independent variable τ.

# Details 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 {n,n}, {n,p}, {q,n}, {q,p}, and {n,n}.
• 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 xi0 and uj0 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

# Examples

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## Basic Examples(5)

A state-space model of an integrator:

 In:= Out= A secondorder single-input, single-output system:

 In:= Out= The state-space model of a transfer-function object:

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

 In:= Out= The state-space model of a set of ODEs:

 In:= Out= ## Properties & Relations(14)

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