WIP: Add `SampledTime` operator

[baggepinnen]

This PR implements the SampledTime operator proposed by @jonniedie in https://github.com/SciML/ModelingToolkit.jl/issues/894#issuecomment-805893878

It provides a convenient interface between the continuous and discrete time domains, examplified by

julia> @variables t x(t);

julia> k = SampledTime(t, dt=0.1);

julia> x(k)
  Sample(t; dt=0.1)(x(t))

julia> x(k+1)
  Shift(t, 1; dt=0.1)(Sample(t; dt=0.1)(x(t)))

i.e., the semantics is that when you call a continuous-time signal with this operator it becomes sampled, and possibly shifted. If the indexed signal is already a discrete-time signal, the Sample should be a noop.

This PR builds on

• #1382

[ValentinKaisermayer]

If x(k) is the value of x at the current time step, I think any x(k+n) with n>0 is not implementable. Modelica only defines the previous(.) operator x = A*previous(x) + B*u.

[baggepinnen]

I think any x(k+n) with n>0 is not implementable

Being able to express a model is not the same as being able to implement or simulate it, I see no reason to limit the expressivity the way modelica does. The model

x(k+1) = x(k)

defines a constant system, which is trivially implementable. In general, for discrete-time systems you may transform all shifted variables by shifting them with the largest shift present and then you have a causal system you can implement, it doesn't matter if the way the model was written was not implementable.

Also, you often want to express non-causal / non-proper models which are later inverted, thus becoming causal/proper. This is common when you design model-based inverse filters for feedforward design.

[ChrisRackauckas]

If x(k) is the value of x at the current time step, I think any x(k+n) with n>0 is not implementable

That could actually be useful for PDE definitions.

[baggepinnen]

If x(k) is the value of x at the current time step, I think any x(k+n) with n>0 is not implementable

That could actually be useful for PDE definitions.

Good point, perhaps SampledTime is a poor choice of name, maybe it should just be called SampledVar or something more generic to indicate that the independent variables does not have to be time.