SystemsModelDelay ()

SystemsModelDelay[]
represents a time delay of in a StateSpaceModel or TransferFunctionModel.

DetailsDetails

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

ExamplesExamplesopen allclose all

Basic Examples (3)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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