Conditions for expressing a system as difference equation

1. What is a system of difference equations?
2. How do you tell if a system is stable from the difference equation?
3. What is difference equation in control system?

What is a system of difference equations?

An equation that shows the relationship between consecutive values of a sequence and the differences among them. They are often rearranged as a recursive formula so that a systems output can be computed from the input signal and past outputs.

How do you tell if a system is stable from the difference equation?

3.1.

The equilibrium point u^* is said to be stable if all the solutions of the above difference equation approaches to b1−a b 1 − a as n becomes large.

What is difference equation in control system?

From the digital control schematic, we can see that a difference equation shows the relationship between an input signal e(k) and an output signal u(k) at discrete intervals of time where k represents the index of the sample.