The inputs that will be provided to the system will be defined over discrete time,

K. Let's call the input to the system,

V. So this V is a function of K,

and a different case might have different values.

So let's say that this is the value of K equals zero.

This is the value of K equals 1.

This is K equals 2, K equals 3, K equals 4.

What we expect to

have is an output but to also define a discrete time instance.

You may notice that's K. And the first value of

the output will also depend on what is called

the initial state of the discrete time system.

This state is typically a vector that captures

all the meaningful variables of this system in order to describe these change over time.

So given an initial state and initial input,

so this will be V at zero in initial state,

then you can actually compute what the initial value would be.

Or in some situations,

you can actually assign an arbitrary,

depends on the type of model you're thinking of.

Let's say that the output of these is these Greek symbol, theta.

Now, in order to compute the new value at time equal 1 of that output,

then we will need to use the information

of the input at time equals 0 of the initial state.

So let's say that this value right here is the result of using these values

here along with this value here.

This is what provides this information here.

And you can keep doing this for every K. So you can

actually generate a signal of the output that will

depend on the previous value of this state and the previous value of the input,

and you can continue these typically over all K. So this case,

remember, take value in that set.

The question is, what is the most efficient or

a good way to actually relate this input-output signals?

And the way that we're discussing this course is

a difference equation model.

In a difference equation model,

we are given a function.