SystemsModelDelay

SystemsModelDelay[δ]

represents a time delay of δ in a StateSpaceModel or TransferFunctionModel.

Details

  • SystemsModelDelay[δ] makes it possible to represent systems involving time delays and efficiently manipulate, approximate, and simulate these systems.
  • SystemsModelDelay[δ] is typeset in StandardForm as δ and can be entered using delay.
  • For a StateSpaceModel, SystemsModelDelay[δ] can occur linearly in any of the system matrices. For a signal , SystemsModelDelay[δ]w[t] is taken to be .
  • For a TransferFunctionModel, SystemsModelDelay[δ] can occur linearly in the coefficients of the polynomials. It is taken to represent a transformed time delay:
  • -δ sin a continuous-time system
    z-δin a discrete-time system
  • Here, s is the Laplace-transform variable, and z is the z-transform variable.
  • For discrete-time systems, the delay δ is taken to be a multiple of the SamplingPeriod.

Examples

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Basic Examples  (3)

A state-space model with an input delay:

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A transfer-function model with delay:

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A time-delay state-space model created from delay differential equations:

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Scope  (7)

Applications  (1)

Properties & Relations  (5)

Possible Issues  (1)

See Also

StateSpaceModel  TransferFunctionModel  DiscreteShift

Introduced in 2012
(9.0)