 |
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[tfm]
gives a state-space realization of a TransferFunctionModel tfm.
StateSpaceModel[{f, g}, {{x1, x10}, ...}, {{u1, u10}, ...}]
gives the state-space model obtained by Taylor linearization of 
, or 
, about the point 
.
StateSpaceModel[eqns, {{x1, x10}, ...}, {{u1, u10}, ...}, {g1, ...}, 
]
gives the state-space model obtained by Taylor linearization about the point 
of the differential or difference equations eqns with outputs 
and independent variable .
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 can be specified as StateSpaceModel[{a, b, c, d}, SamplingPeriod->]. - 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-> ]
- 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}] 
- For equational input, default linearization points
and 
are taken to be zero. - The following options can be given:
-
SamplingPeriod None the sampling period StateSpaceRealization Automatic the canonical realization DescriptorStateSpace Automatic standard or descriptor realization SystemsModelLabels None the labels for the input, output, and state variables - When converting from transfer-function model tfm, the controllable realization is used.
Examplesopen all
Basic Examples (5)
A state-space model of an integrator:
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A second-order 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 :
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The state-space model of a set of ODEs:
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