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docs/src/examples/delay_systems.md

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Time-delay systems are numerically challenging to simulate, if you run into problems, please open an issue with a reproducing example. The [`lsim`](@ref), [`step`](@ref) and [`impulse`](@ref) functions accept keyword arguments that are passed along to the ODE integrator, this can be used to both select integration method and to tweak the integrator options. The documentation for solving delay-differential equations is available [here](https://diffeq.sciml.ai/latest/types/dde_types/) and [here](https://diffeq.sciml.ai/latest/tutorials/dde_example/).
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## Estimation of delay
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See the companion tutorial in ControlSystemIdentification.jl on [Delay estimation](file:///home/fredrikb/.julia/dev/ControlSystemIdentification/docs/build/examples/delayest.html). This tutorial covers the both the detection of the presence of a delay, and estimation of models for systems with delays.
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See the companion tutorial in ControlSystemIdentification.jl on [Delay estimation](https://baggepinnen.github.io/ControlSystemIdentification.jl/dev/examples/delayest/). This tutorial covers the both the detection of the presence of a delay, and estimation of models for systems with delays.
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## Approximation and discretization of delays
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Delay systems may be approximated as rational functions by means of [Padé approximation](https://en.wikipedia.org/wiki/Pad%C3%A9_approximant) using the function [`pade`](@ref). Pure continuous-time delays can also be discretized using the function [`thiran`](@ref). Continuous-time models with internal delays can be discretized using [`c2d`](@ref), provided that the delay is an integer multiple of the sampling time (fractional delays are not yet supported by [`c2d`](@ref)).

docs/src/examples/zoh.md

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# Analysis of sampled-data systems
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A sampled-data system contains both continuous-tiem and discrete-time components, such as a continuous-time plant and a discrete-time controller. In this example, we will look at how to analyze such systems using the ControlSystems.jl package. To learn more about the theory of sampled-data systems, consult the reference mentioned at the end of this page.
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A sampled-data system contains both continuous-time and discrete-time components, such as a continuous-time plant and a discrete-time controller. In this example, we will look at how to analyze such systems using the ControlSystems.jl package. To learn more about the theory of sampled-data systems, consult the reference mentioned at the end of this page.
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First, we analyze the effect of ZoH sampling in continuous time and compare it to the equivalent discrete-time system
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docs/src/lib/constructors.md

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thiran
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ControlSystemsBase.seriesform
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```

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